What do you mean by Nitrogen fixation?

Nitrogen fixation:

• It is an essentially biological process and the initial stage of the nitrogen cycle. 
• Plants cannot directly use Nitrogen gas present in the atmosphere. It needs to be fixed into the soil. It is done by certain bacterial species like Rhizobium, Azotobacter, etc. and by other natural phenomena. Thus, Nitrogen in the atmosphere is converted into ammonia (another form of Nitrogen).
• Converted Nitrogen or Ammonia will be synthesized by plants using various elements which they obtain from the atmosphere as well as from the soil.

It's basically the industrial process or natural process of converting nitrogen gas of atmosphere into another form of nitrogen, e.g. ammonia.
In the natural process, there are many converted by numerous microorganisms; whereas in the manmade, i.e. Industrial process which is also popularly known as Haber's process, converts H2 and N2 into NH3 in the presence of a catalyst, e.g. Fe(iron).
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Nitrogen fixation is a biological or chemical process that is carried out by some legumes like Pisum sativum, clover, soybeans, alfalfa etc. These plants need nitrogen to make proteins, nucleic acids and amino acids, which they cannot do by themselves. The chemical nitrogen fixation takes place during lightning that heats the air and converts atmospheric nitrogen and oxygen into oxides of nitrogen which later reacts with water and seeps into the soil, and can be used by the plants.
In biological nitrogen fixation, the legumes harbour nitrogen-fixing bacteria like Rhizobium in the nodules of their roots. These bacteria possess a symbiotic relationship with the plant and convert atmospheric nitrogen to ammonia or other nitrogen compounds, by their nitrogenase enzyme, which can be assimilated by the plants later. The fixed nitrogen is released when the plants die and make it available to other plants and fertilize the soil. Biological nitogen fixation was discovered in 1877 by Theophile Schloesing and Achille Muntz.

To produce proteins, leguminous plants like pea require atmospheric nitrogen. But, they cannot directly get nitrogen from the air. To overcome this problem, they undergo a symbiotic relationship in which certain rhizobium bacteria at their root nodules convert atmospheric nitrogen into soluble nitrate salts, such that the plant could efficiently conduct it. This process is known as nitrogen fixation.

Nitrogen is an essential component in DNA, RNA& protein. So nitrogen is vital for all living organisms. In our atmosphere, 78% nitrogen is available. But this molecular nitrogen is highly stable and non-reactive. So living organisms can not use this nitrogen.
Some bacterias(they are present in soil & roots of the plants) are capable of converting this nitrogen into the reactive form of ammonium or nitrates. So this process of breaking nitrogen atom from nitrogen molecule and fixing with hydrogen or oxygen is called a nitrogen-fixing process.
After the nitrogen fixation, plants are getting nitrogen. We are consuming the plants and getting the nitrogen.