1TB means 1 TeraByte, or rather, 1024GB.
The 1TB is 524GB bigger than 500GB.
The faster portion depends on the type of hard drive the two are.
For example, your 500GB drive could be 4200 RPM and the 1TB could be 7200 RPM. The higher the RPM, the quicker it is. RPM stands for Revolutions Per Minute. The RPM numbers are examples, so you'll have to refer to your manufacturer's guide on how much the RPMs are for each of your drives.