I'm assuming here (as explained here) that the essence of what Jesus did was to make possible resurrected eternal life in Heaven.
One way I think about resurrection is that Jesus described himself as the Good Shepherd, and developed the explanation that we were like sheep who could follow him - implicitly from biological death of the body, to eternal resurrected life.
I take this parable rather 'literally' as describing a 'process' or transformation - happening through time - which we may choose to go-through after death.
It seems, from the Fourth Gospel, that the process is one in which it is necessary, in some sense, to follow Jesus; and that this following happens (broadly) because we love Jesus and have faith in his promises.
This raises the question of why is it necessary to follow Jesus; why cannot at least some Men find their own way?
One answer is that Jesus's own death and resurrection 'blazed the trail' which Men coming after were then able to follow - metaphorically, Jesus created or 'cleared' a path from mortal to immortal life; and afterwards this path was enough for Men to follow.
However, I am convinced that Lazarus was resurrected by Jesus before Jesus himself had undergone the transformation. If correct; this means that Jesus made possible resurrection for those who loved and believed him even before he himself died.
When did resurrection become possible? At the time of Jesus's baptism by John- when he began his ministry and became fully divine and capable of primary creation, as demonstrated by the miracles and direct interaction with God The Father.
In other words, Jesus's death and resurrection was 'only' a matter of providing him with an immortal body; because he had already - even while still mortal - made the eternal spiritual commitment to live in total harmony with God's creative motivations.
Putting these together; it suggests that resurrection was made possible by Jesus, a Man, attaining fully divine creative ability; and this itself is an aspect of Jesus (from his baptism) living (yet still a mortal Man) in permanent and complete harmony with the will of God the primary creator.
When other Men than Jesus (e.g. but not exclusively saints) have done miracles; these happened because the miracle worker was - at that moment, but temporarily - in harmony with God's will.
The difference between Jesus after baptism and other Men was that Jesus (while still mortal) had made a permanent and irreversible commitment to live in total harmony with God's creation; and we men are not able to make this permanent commitment during mortal life - but only afterwards, after biological death, and by means of following Jesus.
I have not really answered the question of what it is that Jesus uniquely does to enable us to choose resurrection; but perhaps the analysis provides some extra focus and specificity.
What happens to enable resurrection is this choice to allow ourselves to be made wholly harmonious with God's divine creative will.
This is mostly a positive desire to be resurrected, to dwell eternally in Heaven; but also vitally, 'double-negatively', it entails a willingness to discard our sins. That is, desiring to be cleansed of all our motivations that are Not aligned-with God's creative will.
Thus, to enter Heaven we must want to enter Heaven, and as party of this, we must want to be transformed such as to remove all aspects of ourselves that are hostile to Heaven. And we must want these permanently.
Until Jesus; no Man had ever been in the position of loving God so fully that he was able (or willing) to make this total and permanent commitment.
But after Jesus had made this commitment; reality was changed forever for those who loved Jesus and wished to follow him.
The crucial difference between Jesus and us, is that we cannot (as he did) make eternal commitments while still mortal; we can only make such commitments after biological-death. The 'entropic' nature of our-selves (including our minds and wills), and of this world, seem to render all permanence impossible to us.
There may perhaps be some exceptions, as with some (not all) of the true saints: so, perhaps some mortal Men can (since Jesus) love him perfectly enough to make an eternal commitment?
But for most of us, we are too labile and corruptible; and we are provided-for by having the final choice made post-mortal, at a time when we have become discarnate spirits.
All we have to do in mortal life is decide whether we want resurrected life in Heaven; and know that this is possible for any who choose to follow Jesus Christ's guidance on this path; and we can do this with the help of the Holy Ghost - who is the spirit of Jesus active in this world.
By this account - the deep meaning of Grace, is that this was done for us by Jesus Christ; and we need merely to assent; rather than having to find the path to resurrection by-ourselves.