By mechanical media I mean whatever is intended to physically catch particles in the water. Generally it's a pad or filter floss. Not sure what bio max is but it sounds like biological filtration, ceramic rings, clay pellets, bioballs etc. You generally never have to clean biomedia if it comes after mechanical filtration in terms of the direction of water flow through the filter. You also never expose it to anything other than tank water, or you risk 'uncycling' your filter. If you ever need to clean it just shake it off in some old tank water (i do this with my mechanical media because i'm cheep).
Just in case you don't know, there are 3 basic types of filtration for freshwater: mechanical, chemical, and biological(aka bio) filtration.
Mechanical collects debris the filter sucks up and goes first in terms of what the water contacts first and is always sorted from course to fine(not all filters have space for multiple pads).
Next is the chemical filtration, which is completely optional and consists of activated carbon (nitrate, phosphate, and ammonia media is available but I strongly advise against it, not only is it a waste of money but they do funky things to your chemistry).
Last is your biological media. This provides a substrate for your bacteria to grow. This is the media that turns your ammonia into nitrate and the most important part of the filtration. It can be anything from clay pellets, bio balls, ceramic rings, large gravel, course mechanical media. Some people even employ the use of fluidized sand beds which are very efficient but often more trouble than it's worth. Because biomedia is filled with living organisms, it NEVER comes into contact with anything other than tank water. Many people combine bio and mechanical media, but they often experience ammonia spikes when replacing media.