The array module is kind of one of those things that you probably don't have a need for if you don't know why you would use it (and take note that I'm not trying to say that in a condescending manner!). Most of the time, the array module is used to interface with C code. To give you a more direct answer to your question about performance:
Arrays are more efficient than lists for some uses. If you need to allocate an array that you KNOW will not change, then arrays can be faster and use less memory. GvR has an optimization anecdote in which the array module comes out to be the winner (long read, but worth it).
On the other hand, part of the reason why lists eat up more memory than arrays is because python will allocate a few extra elements when all allocated elements get used. This means that appending items to lists is faster. So if you plan on adding items, a list is the way to go.
TL;DR I'd only use an array if you had an exceptional optimization need or you need to interface with C code (and can't use pyrex).