The 8 Bit Counter component behaves somewhat like a register, in that it starts with a value of 0 and can have its value changed.
It has two inputs, an Overwrite Value which can be used to change the counter's value on the next tick; and an Increment/Overwrite toggle. The default behavior is to increment by one on each cycle if an OFF signal is connected to the Increment/Overwrite input. If an ON signal is connected to Increment/Overwrite, it will change the value of the counter to the value that is detected on the Overwrite Value pin.
The output pin is always active, so the current value of the counter is always being output.