N1 and N2 are the rotational speeds of the engine sections expressed as a percentage of a nominal value.
It is similar to the revolutions per minute (RPM) of a piston engine, expressed in percentage instead of in the actual rate of rotation.
They are different because they are characteristic on two-spool engines (see the figure below). The first spool is the low pressure compressor (LP), that is N1 and the second spool is the high pressure compressor (HP), that is N2. The shafts of the engine are not connected and they operate separately.