1.
If something kicks in, it begins to take effect.
As discounts kicked in, bookings for immediate travel rose by 15%...
PHRASAL VERB: V P
2.
If someone kicks in a particular amount of money, they provide that amount of money to help pay for something. (AM)
Kansas City area churches kicked in $35,000 to support the event...
= contribute
PHRASAL VERB: V P n (not pron)
see also kick down