To continue with something. To pick up where you left off. Examples of it's use in a sentence are:
"After lunch he decided to resume the work he had been doing on his science project".
"She saved the word document so she could resume it at a later date".
This use of the word is as a verb.
Resumé (the accent on the last 'e' is often omitted) can also refer to the document used to apply for jobs (sometimes called a CV or "Curriculum Vitae").
It is a listing of your education and previous work experience. This is the French use of the word, with the accent over the 'e' changing the pronunciation of the second part to 'may'. Res-oo-may.