Once you’ve hit Chapter 6, you will be able to join the Expedition Team (which is basically the Rescue Team). In Lively Town you will be able to use the Connection Orb to go on Mission, rank up in on the Team, get points to get stuff and unlock new and awesome Pokemon to recruit.
Be aware that in order to rank up, you will need to go up to the second floor of the Exposition Society Bulding and examin the orb to move up a rank once you have enough points. There are no gimmes in life or in this game, apparently.