To elaborate on Colin's answer...
The word "fells" has a few different meanings, depending on context:
Option 1 is the context of
On the average day, a lumberjack fells a dozen trees.
In that context the word would essentially mean "chops down" or "knocks over".
Option 2 is the context of
The huntsman sold seven fells today.
This usage is largely an archaic remnant of Old English, and was used to mean "an animal's hide/skin with it's hair".
Neither of those make much sense in that excerpt from The Hobbit - which gives us a bit of a clue that it's probably Option 3:
That there field has 3 fells in it.
In which case, it's just another word for a grassy hill (which may, or may not, be big enough to also be called a mountain). Meaning that he's saying that the dwarves live in caves under grassy hills.
Note, that this particular meaning is chiefly British (primarily used in the North of England and Scotland). Considering Tolkien himself wrote during one of the spikes of use for this meaning (and, I believe, he spent much of his life in the main regions the word is used), it reinforces the likelihood of him choosing to use this particular word in this scenario.
He also uses the relatively niche definition of "fell" elsewhere to describe evil forces (i.e. "fell hordes" to mean that the hordes were inhumanly evil).