I love you.

Watashi wa anata o aishiteimasu. : I , you, be loving : I love you.

aisuru : love(verb)
aishiteiru : be loving
aishiteimasu : be loving (polite)

" verb+-shiteiru" means " be+-ing".
A verb is to explain the action.
The function of "-shiteiru" is to explain the current situation of the "verb".

There exists a little bit diffrence between " verb+-shiteiru" and " be+-ing".

Aishiteimasu : ( I ), be loving : I love you / I'm loving you.

Watashi wa anata o eienni aishimasu. : I, you, forever, love : I love you forever.
In above case, "aishimasu" is right. If "aishiteimasu" is used, the meaning of sentense will chang to " I'll be loving you forever.".

Similar case;
shiru : know
shitteiru : (literaly means " be knowing" ) know

Watashi wa sore o shitteimasu. : I, it, know : I know it.