Is it common to review papers assigned to your supervisor?
It is not uncommon for the advisor to ask a student to review a paper. Let's face it — reviewing is a chore, takes a huge chunk of your time and most people do it not out of interest for the paper, but rather a necessity (it factors in promotions within the organization and recognition within the society) and probably some feigned interest in the "role of an academic" and "giving back to the society".

Usually, the papers that an advisor passes on to their students are 


tangentially related to their interests 
only mildly interesting or borderline stuff
are not from top-tier journals


As a student, you should never pass up on these opportunities. It can be a very rewarding experience to review a paper and discuss with your advisor. Some of the things you'll learn are:


that you didn't catch on to some inconsistency/mistake after a month of review, but your advisor did it in 15 mins of casual reading.
to write an effective critique while at the same time not putting the authors down. Contrary to what many may think, a review is not all about "your math sucks!". While yes, it should be pointed out if it indeed sucks, there are ways of saying that. If you spend a lot of the review finding faults, then it is also "fair" to throw in a couple of nice things about the paper and balance it. 
you'll also learn to not nit pick on minor quibbles and focus on the technical content (I hate it when a reviewer makes a huge deal of 'data are' vs 'data is').
You'll learn to do this while juggling other activities, so it's also an early lesson in time management.


In the end, the quality of the review is partly your advisor's responsibility and he's not going to allow it if it is completely shabby. So, take this as an opportunity to learn about how to write a review.

Speaking for myself, I reviewed a couple of papers for my advisor in my early years and now, after I have a few publications to my name, I get invited to review papers on my own (i.e., not via my advisor). Recently, there were a couple of opportunities that my advisor passed on to me, but the difference this time, is that he trusts me to do a decent review and so requested the editor to officially ask me to review, so that I'll get credit for it.