EDTA is a chelating agent. Put simply Fe-EDTA makes it possible for iron to be available in a nutrient solution in which it would otherwise precipitate and become unavailable to plants. Adding ferrous chloride by itself to most plant nutrient solutions would not supply enough Fe to a plant in hydroponics to prevent chlorosis in young leaves, a deficiency symptom. It also to some extent can facilitate Fe uptake by roots. In fact some plant species exude chelating agents into the rhizosphere.
Saurabh , your question is very valid and thought provoking . Let me try this , although , it is more of physiology and biochemistry than exclusive soil science. When Fe-EDTA is used as an chelated source of Fe in a nutrient medium , after crossing the plasmalemmata of cortical cells of roots , migrating to symplasm into the cytoplasm , Fe-EDTA is subjected to metabolic breakdown , where a lot depends upon the pH and pCO2 . thereafter , the iron gets deposited into ferritin , a iron storage protein. In this process , there are involvement of two major enzymes , peroxidase and catalse . The response of root cells to application of Fe-EDTA is accompanied by formation of rhizodermal transfer cells, accumulation of reducing substances in the rhizodermis ,and enhanced proton efflux , faciliatating the uptake of iron to enter further into the cortical cells after crossing through plasmalemmata of root walls. There are many hypotheses about the chemistry of Fe-EDTA , some claim it is broken at soil-root interface , while others claim , the whole molecule is consumed by the presence of large number of iron transporters on the cell walls, which deliver the molecule to go through the same process as I described earlier.
There have been studies to compare the efficacy of Fe-EDTA with synthetic siderophores. However , both the sources produced no discernible differences in plant metabolism . but both of these sources were inferior to non-iron source.
Note that Fe-EDTA is the most well known Iron chelate to supply Fe to plants via the nutrient solutions, but the Fe-DTPA is the most used Iron chelate for this purpose in soilless cultures in Western Europe. The reason is the better pH stability.