At the end of the film's climax, Batman is assumed dead but he has saved Gotham. This time around, everyone knows it was the Batman who acted as their savior. He is memorialized in the form of a statue and his actions are celebrated by the city. Before Bruce leaves Gotham indefinitely, he gets his will and certain things in order, which is how Blake is left with the means to find the cave entrance. It is implied that Bruce has also restored the Batsignal on the roof of the GCPD.
As you know, it's revealed that 'Robin' is a part of Blake's full name, and throughout the film, we have seen how he has been inspired by the Batman's actions. He also struggles with what he CAN and CAN'T do as a cop, including the fact that his job will sometime require him to kill. In the end, after seeing the selfless action of the Batman, he tosses his badge away and leaves the force behind, symbolically beginning his journey of becoming something 'more' than a cop. This mirrors Bruce throwing away the gun in BB. I think that moment in BB is when Bruce 'became' Batman, and this moment in TDKR is when Blake 'becomes' Robin.
Batman has seen the good in Blake and recognized the similarities between Blake and himself. Like Bruce, Blake understands the importance of justice and that it often requires the will to act, not just standing back and letting others lead you...but taking control of your destiny. This is why Bruce decides to leave him with the means to do so. We don't know all of the things that Bruce has left 'Robin', but access to the cave and his equipment is one of them.
Here's where my ideas come into play: No, Blake is not ready to just suit up and hit the streets. This is only the beginning of his journey, much like the early events of BB were the beginning of Bruce's. I'm sure that among the other things Bruce left to Blake were instructions or hints at how to train and prepare himself for the things he may encounter. Or, he has trusted Blake to find his own way. That we do not know for sure. We don't even know if Blake will follow through and become this new hero...but I believe he will.
The fact that his full name is revealed also says something to me. Throughout the whole film, he refers to himself as John Blake. He is clearly embarrassed or uninterested in using his full (or real) name. He may have even been bullied for it as a child. But when collecting the bag Bruce left him, the woman asks him for his name. He replies, "John Blake". She then says, "You should use your full name...Robin." He smiles, which to me indicates that he is ready to embrace this other part of him that has remained dormant for some time. So, in my eyes, there's a great chance that Blake will use the means provided to him to create a NEW symbol for Gotham, one that he can make his own. He can build his own reputation, much like Bruce created his own. OR he can choose to take the symbol of the Batman and allow that symbol to live on. The whole city believes Batman to be dead and gone, but if he were to return and that signal was to shine again, it would prove that the Batman is immortal in the eyes of Gotham (and this is partially true since Bruce survived).
It's completely left to interpretation and can be debated for the next century. ALSO, the fact that Bruce is clearly still alive and well led me to imagine that someday he would return...when he is ready. He could return to Gotham and train Blake in secret, or he could simply return to aid him in a time of need. IMO, there are many more stories to be told in Nolan's Batman universe. We just will never see them...but, we can imagine them.
This is what I love about the ending. People are panicking about the Robin thing or Blake potentially become Batman, but it's no different than Bruce training and fighting alongside a 13-year-old orphan. IMO, this version of Robin is much more realistic and Blake does EARN this trust from Bruce. They share a special bond during the film, and Bruce clearly deems him worthy of becoming a part of his world.
In Batman Begins, Bruce sets out on this journey of finding himself. He does find himself and, over the course of the trilogy, experiences success, failure, pain, and redemption -- a complete story arc that is stretched over three films. Bruce has done what he needed to do. He's happy...for now. He's moved on from Gotham...for now. We do not know if he will return, but he's already given so much to the people of Gotham. Maybe he's content with remaining in the shadows for the rest of his life. But in my eyes...probably not. Still, for now, he has helped set another man on a path towards redemption and self-sacrific. I loved it. This is how I described it to the one person so far that I told the ending to:
One journey ends. Another begins.
