Mamta D and TRomano have done a good job explaining the construct and the meaning of the phrase.
I'd like to add what the words mean. (I can see why this particular case might be confusing, because the two words might seem to be nearly synonymous, and one can find many different definitions when you look these words up in the dictionary.)
For look, we want Definition #2 (of 8) in Macmillan:
look (v.) to search for someone or something
And for see, we want Definition #5 (of 16) in Collins:
see (v.) to ascertain or find out (a fact)
I'll look and see if I have any sugar in the cupboard.
I'll search for sugar in the cupboard, and [as a result of that search] find out if any sugar is there.
Note that this could be shortened to:
I'll see if I have any sugar in the cupboard.
with minimal loss of meaning.