Why is the nitrogen fixation carried out by cyanobacteria , bacteria and some archaea in marine environments important?

The nitrogen fixation is a very important process because it is the principal source of nitrogen in the marine environment for photosynthetic plants. Nitrogen is a growth limiting nutrient, that is very important for the growth of photosynthetic plants. During the process of nitrogen fixation, nitrogen is absorbed from the atmosphere and it is fixed by nitrogen fixing organisms. 

The nitrogen fixing performed by cyanobacteria and some archaea transforms nitrogen in the form of N2, which is very common, into the form NO3 and NH4, which are much less common. This is important because most ocean plants -- particularly the plankton that makes up the majority of oceanic plant life -- need nitrogen in order to transform sunlight into energy but cannot use it in the common N2 form. So the nitrogen fixation carried out by cyanobacteria and archaea transform nitrogen into a form in which it is usable by other ocean organisims.