The Son, the Second Person of the Trinity, is now in his rightful place, able to fully exercise the power and authority of his godhood. That's what "sitting at the right hand" means. It's not a literal statement that Jesus is just sitting on a far-off throne, but rather an active statement of his relationship to the Father and his position over the rest of creation. But, what exactly does he do now? He did all the important work by going to the cross, didn't he? Well, yes, the atoning work is done, but there are at least two other very important jobs Jesus has.
First, Jesus is continually acting on the behalf of those who have put their trust in him. He's our advocate, very much like an attorney, ensuring a fair hearing before the Great Judge. However, let's not harbor an image of some highly paid, well-dressed flunky. A lawyer in an earthly court must, to a large degree, act in accordance with the client's wishes, even if the lawyer does not agree that those wishes are in the client's best interest. The client has all of the authority; the lawyer is a necessary tool. This is quite the opposite of our relationship with Jesus. He will only plead the case of those who have surrendered all of their authority. "Trust in him" is not just a catchphrase. It's an absolute necessity in order for Jesus to effectively work for our good.
Not the least of these good works is the final step in the atonement process. Before we commit ourselves to Christ, we have no advocate. In the end, there is no defense to make before God. There's no jury to convince. There's no room for doubt. We're guilty, period. As we've discussed before, there's only one sentence: eternal death. It's at this point in the heavenly courtroom that Jesus steps in. "He's one of mine, Your Honor. You will find that sentence has already been carried out. He's fully covered, paid in full." Then, the Father, with the voice that spoke everything into being, absolute power mingled with absolute love, says, "You're free". The Bible paints a picture of unimaginable celebration every time those words are spoken on behalf of the least one of us.
The second important job Jesus has is somewhat mystical. In some way, the Bible tells us, he actually embodies his entire people. This body is "The Church". This is not just a convenient label. In a completely non-mystical way, the Church is the conduit through which Jesus' work is done on earth. Yes, miracles happen, but they always occur where there is a faithful person to interpret the miracle as coming from God and respond in a practical, personal manner. Miracles by themselves accomplish nothing. There must always be someone there to place the miracle in the context of God's power and will. This has been true of every recorded miracle, from Genesis to the present.
But, most of Jesus' work is done through our everyday interactions. We are his eyes, his hands, his legs in this world. He can only reach out to people through the Church. The amount of influence he can exercise in this world is very much limited by our willingness to follow his example, to discern his will. It is no small part of the sins we commit that are sins of omission, simply not doing what we know we should do. We want to grab those reins of authority and steer ourselves where we want to go, down the easy road. One of the hardest tasks in the Christian life is letting Jesus drive our car, right through all the warning signs, stoplights, oncoming traffic, and off-road adventures. But, in the end, we aren't rewarded for having the shiniest paint job. The highest praise is for those who simply believe, and trust, and act in His name.