"to concur" basically means to agree with someone. For example:
"Marcus thinks we should get rid of this painting."
It comes across as quite formal, however, and would be used mostly in academic-style writing (such as the example you posted). Most of the time people would simply say "I agree."
"to update" something means to make it more modern or current or to make a newer version of something. For example:
"My computer is crashing a lot. I really need to update my software."
In the context of the text above, the author is talking about how humans modify (or update) how they feel about their choices. Basically it is saying is that once we choose between two possible options, we tend to increase how much we like the option we chose so that our opinion of the choice agrees (concurs) with the choice itself, since otherwise we would keep going back and forth between the two options forever and never make up our minds. In a way it is saying we tend to convince ourselves we made the right choice after making it so that we feel good about the choice we made. This way of changing (or updating) our thinking minimizes any self-doubt we might have about our actions.
I hope that helps!