Suffered under Pontius Pilate,  was crucified, died, and was buried

An essential teaching in Christianity is the crucifixion and death of Christ. Christians teach that the death of Christ was for the purpose of making propitiation for our sin, reconciling us to God, and paying the price for our sins in our place. The Westminster Confession of Faith states;

The office of Mediator the Lord Jesus did most willingly undertake; which that he might discharge, he was made under the law, and did perfectly fulfill it, was prosecuted by Pontius Pilate, endured most grievous torments immediately in his soul, and most painful sufferings in his body, was crucified, and died, was buried, and remained under the power of death, yet saw no corruption.
Westminster Confession of Faith VIII. Of Christ the Mediator

The prosecution, crucifixion, death, and burial of Christ is a historical event that actually happened.

Christ was crucified by Pontius Pilate?

According to the Bible and historians, there was a governor of Judea named Pontius Pilate. The gospel writers wrote that Christ was tried in the court and convicted by Pilate as a criminal. This conviction led to Christs execution. The death penalty in the Roman times was carried out by crucifixion. While the account that Jesus was crucified may only be verified by the gospel writers. It is a historical fact that Pontius Pilate was the province in Judea and that the common form of execution was crucifixion. This can be verified in history books written by Philo and Josephus.

The apostle John, in his gospel, said,

There they crucified Him, and with Him two other men, one on either side, and Jesus in between.
(John 19:18 NAS)

Not just Christ was crucified in this manner; but, many people who were convicted were executed this way. The reason for Christ being prosecuted by Pontius Pilate was to show that, Christ, who was innocent of the charges against Him, was convicted by not only the Jewish community, but society as a whole. The Heidelberg Catechism puts it like this:

Q. 38. Why did he suffer “under Pontius Pilate” as his judge?
A. That he, being innocent, might be condemned by an earthly judge, and thereby set
us free from the judgment of God which, in all its severity, ought to fall upon us.
Heidelberg Catechism Question #38

Christ died for our sins

The purpose of Christ’s death was to act as a substitutionary atonement for our sins. Christ was innocent and did no wrong. He payed the penalty required by God in our place.

For Christ also died for sins once for all, the just for the unjust, in order that He might bring us to God, having been put to death in the flesh, but made alive in the spirit;
(1Pe 3:18 NAS)
For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures,
(1Co 15:3 NAS)
Surely our griefs He Himself bore, And our sorrows He carried; Yet we ourselves esteemed Him stricken, Smitten of God, and afflicted. But He was pierced through for our transgressions, He was crushed for our iniquities; The chastening for our well-being fell upon Him, And by His scourging we are healed.
(Isa 53:4-5 NAS)

God in the Old Testament made it clear that a sacrifice was to be performed as a substitute for the sins of the people.

For the life of the flesh is in the blood, and I have given it to you on the altar to make atonement for your souls; for it is the blood by reason of the life that makes atonement.
(Lev 17:11 NAS)

The New Testament writers made it clear that bulls and goats cannot make atonement for sins.

For it is impossible for the blood of bulls and goats to take away sins.
(Heb 10:4 NAS)

Only Christs one time sacrifice is required to forgive the sins of the people now and forever more.

By this will we have been sanctified through the offering of the body of Jesus Christ once for all. And every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins; but He, having offered one sacrifice for sins for all time, sat down at the right hand of God,
(Heb 10:10-12 NAS)

Christ’s propitiation for our sins

Christ Himself made the propitiation for our sins. Propitiation means Satisfaction. In this case, satisfying the legal requirement each person owes to God for breaking Gods commandments. The writers of the New Testament state:

whom God displayed publicly as a propitiation in His blood through faith. This was to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed;(Rom 3:25 NAS)
Therefore, He had to be made like His brethren in all things, that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people. For since He Himself was tempted in that which He has suffered, He is able to come to the aid of those who are tempted.
(Heb 2:17-18 NAS)
and He Himself is the propitiation for our sins; and not for ours only, but also for those of the whole world.
(1John 2:2 NAS)
In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins.
(1John 4:10 NAS)
and walk in love, just as Christ also loved you, and gave Himself up for us, an offering and a sacrifice to God as a fragrant aroma.
(Eph 5:2 NAS)

The relationship between man and God is broken due to our sin against God. We cannot stop sinning against God and in no time in our life will we ever be righteous in our own deeds. The Heidelberg Catechism states this well saying:

Q. 40. Why did Christ have to suffer “death”?
A. Because the righteousness and truth of God are such that nothing else could make reparation for our sins except the death of the Son of God.
Heidelberg Catechism Question #40

Christ reconciled us with God

Christs death on the cross reconciled us to God. That means Christ gave to God everything we are required to pay to God. Christ repaired our relationship with God.

For if while we were enemies, we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life.
(Rom 5:10 NAS)
He made Him who knew no sin to be sin on our behalf, that we might become the righteousness of God in Him.
(2Co 5:21 NAS)
yet He has now reconciled you in His fleshly body through death, in order to present you before Him holy and blameless and beyond reproach–
(Col 1:22 NAS)
I have been crucified with Christ; and it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me, and delivered Himself up for me.
(Gal 2:20 NAS)

Simply put, everything we owe God, Christ gave to God on our behalf, so we can have a relationship with Him.

Christ paid the price for our sin

It is just like someone owing a large sum of money to the bank. Christ comes up and pays the debt, fixing the credit and the relationship between the one who owes the money and the bank. Except in this case we owe God. He paid our ransom. The ransom is the price of a life. Our life was required by God as a penalty to our sin and Christ paid it.

For even the Son of Man did not come to be served, but to serve, and to give His life a ransom for many.”
(Mar 10:45 NAS)
who gave Himself as a ransom for all, the testimony borne at the proper time.
(1Ti 2:6 NAS)

Christ was placed in a tomb or otherwise stated “buried”

This part is confused by some; however, the Bible is clear. Christ was not buried at all. He was placed in a tomb. In other words, they did not dig a hole and throw His body in it and cover Him with dirt. The Bible says,

and laid it in his own new tomb, which he had hewn out in the rock; and he rolled a large stone against the entrance of the tomb and went away.
(Mat 27:60 NAS)
And when his disciples heard about this, they came and took away his body and laid it in a tomb.
(Mar 6:29 NAS)
And he took it down and wrapped it in a linen cloth, and laid Him in a tomb cut into the rock, where no one had ever lain.
(Luk 23:53 NAS)
Therefore on account of the Jewish day of preparation, because the tomb was nearby, they laid Jesus there
(John 19:42 NAS)

By buried, the creed is expressing that He was dead. Dead enough to be placed in a tomb. The Heidelberg Catechism states it well.

Q. 41. Why was he “buried”?
A. To confirm the fact that he was really dead.
Heidelberg Catechism Question #41