Since we are only talking about the spiritual, that the historical changes happened, are as-read.
We had direct access to God before; ask the Hebrews.
Having to go through Jesus is not direct access to God. Jesus is in between.
So, again, what changed?
Here we go again. The Hebrews did not have universal direct access to God. It was conditional and available to only a few. That was why they needed a High priest to address God on their behalf. Jesus is the reason why we have access. In the new covenant (testament) for the first time we have a direct relationship to God through the Holy spirit which lives in the heart of the believer. Even if Jesus is thought of as in between since he is God then there is no issue here. Since only in the new testament is the holy spirit guranteed as a permanent posession on conversion and the Holy spirit is God then there is no question we have a direct relationship with God. That is why the temple curtain was ripped when Jesus died. It says specifically the barrier between God and man was removed. As well as no more need of the blood of bulls and goats, written law, etc.
And yes the veil was a symbol for seperation between God and man.
Wesley's Notes
27:51 Immediately upon his death, while the sun was still darkened, the veil of the temple, which separated the holy of holies from the court of the priests, though made of the richest and strongest tapestry, was rent in two from the top to the bottom: so that while the priest was ministering at the golden altar (it being the time of the sacrifice) the sacred oracle, by an invisible power was laid open to full view: God thereby signifying the speedy removal of the veil of the Jewish ceremonies the casting down the partition wall, so that the Jews and Gentiles were now admitted to equal privileges, and the opening a way through the veil of his flesh for all believers into the most holy place. And the earth was shaken - There was a general earthquake through the whole globe, though chiefly near Jerusalem: God testifying thereby his wrath against the Jewish nation, for the horrid impiety they were committing.
Barne's notes on the bible
The vail of the temple - This was doubtless the veil, curiously performed, which separated the holy from the most holy place, dividing the temple into two apartments,
Exodus 26:31-33.
In twain - In two pieces or parts. This was the time of day when the priest was burning incense in the holy place, and it is probable that he witnessed it. The most holy place has been usually considered as a type of heaven, and the tearing of the veil to signify that the way to heaven was now open to all - the great High Priest, the Lord Jesus, being about to enter in as the forerunner of his people. However, about the design of the tearing of the veil, the Scriptures are silent, and conjecture is useless.
And the earth did quake - Or shook. Earthquakes are violent convulsions of the ground, caused commonly by confined and rarefied air. This was probably, however, a miraculous convulsion of the earth, in attestation of the truth that the sufferer was the Messiah, the Son of God, and as an exhibition of wrath at the crimes of those who put him to death. It was not confined to Judea, but was felt in other countries. It is mentioned by Roman writers. The rocks rent - That is, were torn asunder. Rocks are still seen at Mount Calvary thus rent asunder, which are said to be the ones that were convulsed when the Saviour died.
Matthew 27:51 At that moment the curtain of the temple was torn in two from top to bottom. The earth shook and the rocks split.