Depends on your specific situation, as to which of the following apply.  But in general, a quick answer...

a.) External assumes you're testing from the outside ( beyond the corporate firewalls / routers, etc ) 

b.) nternal assumes you've got physical / local access to the network and machines being tested, and are testing from the perspective of someone on the inside of the corporate firewalls / routers.

Now, you could also be referring to the people performing the testing, in which case:

a.) External assumes you're paying someone from the outside (another company) to do the testing.

b.) Internal means you have someone on staff doing the testing.

Clear enough?