Author Jonathan Morris does something a bit different with the Weeping Angels in this story. While their modus operandi in the series is typically to send someone back hundreds of years into the past and feed on the unused potential of the life the person would have lived (it's a weird show) in this case the Angels determine that they would be able to feed more effectively by creating a time paradox.
To this end, they target lawyer Mark Whitaker and send him back only 17 years. This leaves him at a point in time where he is able to cross his own timeline, which has the potential to cause all sorts of complications. Naturally, the Doctor, having a time machine, thinks the easy solution would be to simply rescue Mark from the 1990s, where he's been stranded. However, an additional complicating factor reveals itself, which is that Mark has sent himself a list of things that he must do in the past. These are things that he knows he did, because he remembers them happening. E.g., when he was on vacation in Rome, someone returned his lost wallet to the hotel where he was staying.
So, in this case, if Mark doesn't do these things that are established as part of his personal history, that will unravel the timeline! What a headache!
The Doctor warns Mark against any direct contact with his younger self and that if anything begins to threaten the established timeline, it will give the Angels a signal to find and (I guess?) devour him. And that will have dire implications for the entire universe.
It's an interesting time travel conundrum. It's also a little sad watching the middle-aged Mark reduced to a shadowy presence in his younger self's life, quietly arranging all of his successes. It traps him in this loop, because his life basically ends at 37, when he must start shadowing his younger self and working behind the scenes to make sure things turn out the way he knows they're supposed to. At the same time, he must also be careful not to have much of a life of his own, lest he change history.
I always appreciate it when Doctor Who leans into the time travel aspects of its premise in interesting ways. Unfortunately, the Doctor, Amy, and Rory have quite a reduced role in this as the focus is firmly on Mark and his life and maintaining his timeline. Amy, especially, is given nothing to do in this story, which is disappointing and seems to be a bit of a recurring problem with the Eleventh Doctor tie-ins.