Together, jointly
Co- (and its variants com- and con-) comes from Latin "cum" (with, together) and signals joint action, collaboration, or union. cooperate = work together with others; coexist = exist alongside another; combine = join two or more things; connect = link points together. The core idea is always "more than one acting or being together."
The three forms
The variant depends on the first letter of the root: co- is the most general and modern form (cooperate, coexist, coauthor), com- appears before "p," "b," or "m" (combine, compete, compress), and con- before consonants in general (connect, control, confirm). Co- is the most productive variant in modern English for creating new compound words: co-founder, co-host, co-pilot.