Based on your chaser rank, you can go on more difficult missions and match with people at your own skill level. However, this was not entirely implemented in previous tests, may not be in beta either.
You will be able to move between chaser rank levels with promotion matches. If you lose a promotion match, your chase rank will go down.
There are 6 chaser ranks: Wood Chaser, E < D < B < A < S < G
There are also a total of 5 Divisions in each chaser rank, so you will have to climb up the ladder to reach higher chaser ranks.
Advancement Battles will unlock when you increase number of wins in PVP mission. You can increase Chaser level through the Advancement Battle.