Map executes a block of code for each element in a list and returns a list of the results. The magical variable $_ is set (actually localized so it isn't clobbered outside the block) to each element within the block. Map is _extremely_ powerful when in the hands of the likes of merlyn and friends. (i.e. Schwartzian Transform)
A couple (simple) examples to illustrate:
copy a list (i.e. do nothing same as @b = @a;)

@b = map {$_} @a;

Take a list of numbers (a vector) square them, add them together and take the square root (Euclidian N-dimensional distance):

 $dist = sqrt(eval join("+",map {$_**2} @a));

Explanation of that last one: map squares each element in @a (say 1,2,3,4,5) and returns a new list (1,4,9,16,25) then join makes a scalar "1+4+9+16+25", the eval makes it 55 and finally sqrt returns 7.41619... which is assigned to $dist.

For another example see A minor epiphany with grep and map as well as every piece of documentation on the topic you can get your hands on. I think what did it for me (finally) was Effective Perl Programming by Joseph N. Hall with Randal L. Schwartz. The section (Item 12) is only 4 pages long and also covers grep and foreach but, it was the lightswitch for me.
-ase