In this sentence the particle の is being used with its meaning #2 = nominalize verbs/adjectives.
Reason:
食べる is a verb meaning "to eat."
Adding の after it turns the verb's action into a noun-like concept. In this case, 食べるの means "the act of eating."
- This is needed because the verb 止める is a transitive verb i.e. it needs an object. A verb cannot be used as an object of another verb, so の is needed to nominalize it.
Then we have:
- 食べるのを止めて translating to "stopped eating."