Rizobhium is a genus of Gram-negative soil bacteria that fix nitrogen. Rhizobium species form an endosymbiotic nitrogen fixing association with roots of legumes(plant or fruit or seed in family Fabaceae). To express genes for nitrogen fixation rizobhia requires a plant host, means they cannot independently fix nitrogen hence the name endosymbiotic nitrogen fixing.
In general they are gram negative,motile,non-sporulating rods.
Gram negative means this bacteria's cell wall contains very small layer of peptidoglycan(outside layer of bacteria) that is dissolved when alcohol is added.
Motile means ability to divide into new cells.
Non-sporulating shows its inability to produce spores.
So in short Rhizobhium is a bacteria, that have ability to take atmospheric nitrogen and convert it into a soluble form. This bacteria live in the roots of leguminous plants(like roots of grams,beas,beans etc.) and provide them with nitrogen. In return plants give them food and shelter. So this way rhizhobhium shows a symbiotic relationship.