Question

If a state is outside of the contiguous United States, what does this mean?

Answer 1

It means that it's not directly bordering the vast majority of other States, all of which are bordering each other.

Right now it's Hawaii (which is composed of Islands) and Alaska (separated from the contiguous US by Canada) - all the other states are in the contiguous US.

Answer 2

The "contiguous" part is everything you can reach without leaving
the country.  That part is the big glob of 48 states in the middle of
the continent of North America.  You can drive to anywhere in these
48 states without ever leaving the US for a minute. 

The other two states are non-contiguous ... they don't touch any part
of the 48 states, and you have to LEAVE the 48 states to reach either
of them.  Those two are Alaska and Hawaii. 

To reach Alaska, you have to cross either a part of the Pacific Ocean
or a part of Canada, by ship, car, or airplane.  To reach Hawaii, you
have to cross a big part of the Pacific Ocean, by either ship or plane.