what is the purpose of the agar in the bottom of the petri dish?

Agar is used throughout the world to provide a solid surface containing medium for the growth of bacteria and fungi. Agar is typically sold commercially as a powder that can be mixed with water and used as a growth medium in microbe cultures.
As a gel, an agarose medium is porous and therefore can be used to measure microorganism motility and mobility. The gel's porosity is directly related to the concentration of agarose in the medium, so various levels of effective viscosity can be selected, depending on the experimental objectives.