The 68010 is the successor to the 68000 processor. It has the same pinout, and instruction set. It was intended for an easy way to make existing designs faster without redesign of the hardware or firmware.

Unfortunately, one instruction was changed: move sr,dn changed from a user mode instruction to a supervisor mode instruction. This breaks many old Amiga games and demos. The fix is to replace move sr,dn instructions to move ccr,dn. A one byte patch.

The 010 optimizes single instruction loops containing multiplication and division. According to Motorola, this equals to a frequency upgrade from 10MHz to 12,5MHz.

The main change from the venerable 68000 to the now-obsolete 68010 was the addition of support for virtual memory. A few instructions were added and a couple were modified to support the few extra complications this brought to interrupt handling and address spaces.

I'm not an expert on the processor but I think it must have been introduced simultaneously with the 68851 PMMU support chip, which did the actual logical to physical translation.