When Jesus died on the cross, his body physically expired. His heart stopped beating and he physically died.
His humanity did not go into heaven--that is, not until three days later. So what happened after his death is that his body went into the grave, and his immaterial being went to the place where the righteous had then rested -- i.e., the place of rest within the underworld of Hades.
Peter is very explicit that the body of Jesus went into the grave, and that his immaterial being, which Peter calls the "soul" (Acts 2:27) went into Hades. Peter mentions the event a second time to provide emphasis (Acts 2:31).
Why did not the PERSON go to heaven?
Well, the divine nature of the person did return to his Father (Jn 23:46). But his human nature could not go to heaven, because his eternal life (divine nature) was separated from his body through death. Thus his humanity entered both the grave (material humanity - "body") according to Acts 2:31 and well as entered Hades (immaterial humanity - "soul") according to Acts 2:27.
In other words, his eternal life did not reunite with his body until Sunday morning -- the day of the resurrection.
So the body of the PERSON was broken. That is, eternal life (divine nature) was separated from his humanity. His humanity was further subdivided since his soul was separated from his body (Acts 2:27 and Acts 2:31). That is, his soul was in Hades and his body was in the tomb.
To put it another way, the PERSON subsisted in two natures, and these two natures were split apart when he died on the cross. The humanity was further divided (broken) by the separation of soul (to Hades) and body (to the tomb).
So to summarize, in eternity past his divine nature was sired from the Father (the Old English word here is "begotten" -- that is, the PERSON was begotten by the Father) according to John 1:1-3 and 1 John 1:1-3. This occurred before the world existed (John 17:5). When Mary was later pregnant in Bethlehem, the PERSON then took on human nature, and so the PERSON was born a "second" time with respect to human nature; thus the PERSON subsisted in two natures, which were subsequently split when he died on the cross.
The most remarkable evidence of this venture into Hades is the parallel to the liberation from Egypt. Jesus is the greater Moses. His blood is the paschal lamb that redeems those who are slaves of sin (Egypt). He leads the captives free like Moses. He subsequently renders the powers of sin (Egypt) powerless through the "water" of his eternal life, which goes straight to the Promised Land.
The chart below depicts the illustration.
Please note that Hades = Sheol.
He was in the grave three days and three nights; and of course that was the amount of time that transpired when the Israelites escaped Egypt. Fifty days later, the Old Covenant was given at Sinai; fifty days later the New Covenant was given at Pentecost. The parallels are remarkable.
So the soul of the humanity of Jesus was in Hades (also called Sheol) after his death on the cross. He led the Old Testament believers out of the Paradise of Hades and into the Paradise of Heaven according to Ephesians 4:8-10 in addition to Romans 10:7. These verses from Romans and Ephesians indicate that it was Jesus in the lower parts of the earth or abyss. So Hades was an actual area of confinement deep in the earth, since Old Testament saints did not have the gift of eternal life, thus they "retired" to the rest of the underworld after death; but it was a confinement related to spiritual death, and thus the parallel to Egypt, since it is sin which binds us. (The story of the rich man and Lazarus in Luke 16:19-31 provides a glimpse of this two-compartmented area of the underworld.) So the humanity of the PERSON was the first to emerge (be born) out of spiritual death, and so he is the "firstborn" from the dead (Rev 1:5). By inaugurating the New Covenant "through his blood" (Luke 22:20), he now makes eternal life available to all who believe in him so that they will be able to go directly into heaven (John 3:16 and John 3:36). There is therefore no more place of rest in the underworld after death for the righteous. Our place of rest is our inheritance in heaven (1 Pet 1:3-5), where he lives today.