What happens to the extra electricity (amps) created by an off-grid solar (PV) array?
The charging circuit won't draw much current from the PV cells when the battery is fully charged. If there is current capability left over from the demand at any given time, it's not used. 

Just like a battery doesn't discharge (much) when you don't draw current from it- the voltage will increase towards the open-circuit voltage and the current will drop towards zero. 

Edit: Here is the curve of the cell. Maximum power and no power points are indicated (the far left bottom point is also no power, which would correspond to shorting the cell as mkeith indicates some controllers do).