Priority essentially means the ability of a move to go first in a turn. In a turn, usually it is the faster Pokemon (with higher speed stat) that moves first. However, when a move with priority is used, say for example Quick Attack, then that move will go first regardless of which Pokemon is faster.
For example: A Breloom and Metagross are about to duke it out. By stats, Metagross is faster. If both use moves of normal priority (0 that is) then Metagross would move first. But if Breloom uses Mach Punch, which has +1 priority, then it moves before Metagross does.
Priority can be positive, 0 and even negative by value.
0 priority is the normal priority every move has. Eg.- Body Slam, Thunderbolt etc.
Positive priority (+1, +2 and so on) always goes before moves with 0 and negative priority. Also, a move with a priority of +2 goes before that with +1.
Eg.- Mach Punch (+1), Extreme Speed (+2), Fake Out (+3)
Negative priority (-1, -2 and so on) always goes after moves with 0 and positive priority. Also, a move with priority -2 goes after that with -1.
Eg.- Vital Throw (-1), Focus Punch (-3), Trick Room (-7)
Basically, moves with higher priority go before moves with lower priority. When two moves have the same priority, they are tied and the Pokemon with the higher speed stat goes first, like usual.
Hope I helped!