The names are actually well chosen and partly self-describing.

Mine damage dodge (prohibited):
You put together a fleet with different designs in a way that some mine damage can't be allocated by Stars but is dodged.
Example: 1 scout design (20 armor, no shield) plus 4 destroyers (the destroyer ship slot is below chaff design slot).
Result: Mine damage of 500 points gets distributed in a way that Stars puts 4/5 of the damage onto the first design slot. Thus 400 damage goes to the scout design (which can suck up only 20 damage and 380 damage are lost/dodged)

Mine damage allocation (allowed):
Similar like above the damage of a mine hit is allocated to different designs in the fleet but all damage can be allocated, none is lost/dodged.

Conclusion - So as a rule of thumb:
If all of the damage of a mine hit can be allocated to the ships... everything is fine.
If some damage is dodged... it is considered cheating.