what do you mean by an integral multiple of 360 degrees

Answer: 

We know " 360$°$ is one complete revolution . "
So
An integral multiple of 360$°$ is a whole number of revolutions (clockwise or counterclockwise)  .

As if we have positive numbers as for clockwise rotation and negative numbers for anticlockwise rotation . 

So, if we have 720$°$  , So 2( 360$°$ )  so here 2 is the integral multiple of 360$°$ and positive sign shows the rotation is in clockwise direction 
or
if we have - 720$°$ , So - 2( 360$°$ )  so here - 2 is the integral multiple of 360$°$ and negative sign shows the rotation is in anticlockwise direction