My question is, what exactly is this "heavenly reward"?
The short answer: the reward is that you are with God rather than not.
Since you ask from the Catholic perspective, the reply will be based on the current Catechism1.
About each person getting a different reward.
CCC 1023 Those who die in God's grace and friendship and are perfectly purified live for ever with Christ. They are like God for ever, for they "see him as he is," face to face.
Recall from the Old Testament that Moses himself could not see God face to face. Being with God, forever, is considered a great reward among Catholics and is taught by the Church to be the great reward.
CCC 1021 Death puts an end to human life as the time open to either
accepting or rejecting the divine grace manifested in Christ. The New
Testament speaks of judgment primarily in its aspect of the final
encounter with Christ in his second coming, but also repeatedly
affirms that each will be rewarded immediately after death in
accordance with his works and faith. The parable of the poor man
Lazarus and the words of Christ on the cross to the good thief, as
well as other New Testament texts speak of a final destiny of the soul
- a destiny which can be different for some and for others.
That last line (above) appears to be the teaching that you are referring to in your question. And now for the different rewards:
1022 Each man receives his eternal retribution in his immortal soul at
the very moment of his death, in a particular judgment that refers his
life to Christ: either entrance into the blessedness of heaven - through
a purification or immediately - or immediate and everlasting damnation.
The reward is one of three things: entrance into Heaven immediately, entrance into Heaven after purification, or "or immediate and everlasting damnation"
It may be hard for us to grasp, given that we are immersed in the physical world and may make analogies to temporal rewards. The Church teaches that the reward at judgment is spiritual in nature: to be with God and to see God as He really is. What greater reward could there be?
"Well done, my good and faithful servant." (Matthew 25:21)
Just to hear those words at judgment would be reward enough.
1 I suggest a review of the articles I cited the Catechism, since they go have references and footnotes. Each article has notations to show its derivation from Scripture, Tradition, and/or teachings of the Fathers and Doctors of the Church.