A very simple example would be rdd.foreach(print) which would print the value of each row in the RDD but not modify the RDD in any way.
For example, this produces an RDD with the numbers 1 - 10:
>>> rdd = sc.parallelize(xrange(0, 10)).map(lambda x: x + 1)
>>> rdd.take(10)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
The map call computed a new value for each row and it returned it so that I get a new RDD. However, if I used foreach that would be useless because foreach doesn't modify the rdd in any way:
>>> rdd = sc.parallelize(range(0, 10)).foreach(lambda x: x + 1)
>>> type(rdd)
<class 'NoneType'>
Conversely, calling map on a function that returns None like print isn't very useful:
>>> rdd = sc.parallelize(range(0, 10)).map(print)
>>> rdd.take(10)
0
1
2
3
4
5
6
7
8
9
[None, None, None, None, None, None, None, None, None, None]
The print call returns None so mapping that just gives you a bunch of None values and you didn't want those values and you didn't want to save them so returning them is a waste. (Note the lines with 1, 2, etc. are the print being executed and they don't show up until you call take since the RDD is executed lazily. However the contents of the RDD are just a bunch of None.
More simply, call map if you care about the return value of the function. Call foreach if you don't.