There are four choices to mapping jobs to processes. You have to consider multi-args, concurrency, blocking, and ordering. map and map_async only differ with respect to blocking. map_async is non-blocking where as map is blocking
So let's say you had a function
from multiprocessing import Pool
import time
def f(x):
    print x*x
if __name__ == '__main__':
    pool = Pool(processes=4)
    pool.map(f, range(10))
    r = pool.map_async(f, range(10))
    # DO STUFF
    print 'HERE'
    print 'MORE'
    r.wait()
    print 'DONE'
Example output:
0
1
9
4
16
25
36
49
64
81
0
HERE
1
4
MORE
16
25
36
9
49
64
81
DONE
pool.map(f, range(10)) will wait for all 10 of those function calls to finish so we see all the prints in a row.
r = pool.map_async(f, range(10)) will execute them asynchronously and only block when r.wait() is called so we see HERE and MORE in between but DONE will always be at the end.