DoT stands for Damage Over Time. This means that instead of immediate damage, it is dealt over a period of time.
Example: Corrupt
Effect DoT: 10 damage over 12 second (2 dmg tick)
This means that instead of 10 damage being dealt instantly, it will be dealt over 12 seconds. By doing simple math, we can figure that each "tick" will do 2 damage, and that there will be 5 ticks.
A Tick means the damage being dealt in a DoT effect. It is dealt in little bursts, such as
You take 2 damage from [enemy]
You take 2 damage from [enemy]
You take 2 damage from [enemy]
You take 2 damage from [enemy]
You take 2 damage from [enemy]
Each of these is called a "tick".