Tick rate usually means how many times a server calculates the state of the world in an online game. So a client can have 300fps, but the server might only calculate 128 ticks per second. If your computer's FPS dips below that of the server's tick rate (or your internet is bad) you start missing information. The client usually calculates things as if it has perfect information, and then when a tick comes in an tells your computer it is wrong, the client corrects itself. So the lower the tick rate on the server, the more times this happens (since your computer has made hundreds of calculations since the last tick came in) and it seems slower / choppier.
Some games solved the low-tickrate / low-fps problem by timestamping user input independently and interpolating to the simulation, i.e. you can still hit things even with just say 10 ticks per second.
