This is the 371st most frequent Russian word.
немного
A little; a bit; slightly.
In this sentence, 'немного' is used as an adverb to indicate a small degree or extent of tiredness.
Я немного устал.
I am a little tired.
Here, 'немного' is used as an adverb to mean a small amount, in reference to the salad.
Съешь немного салата.
Eat a bit of salad.
In this case, 'немного' is used adverbially to describe a short distance farther.