yeah you're right "iru" means to be for (for things that are alive-"aru" for not alive) It can also mean "to need".
When you have a verb in the "te" form and then add the verb "iru" its like saying its an ongoing action. "nemasu" is to sleep, but if you said it I would assume you mean I'm going to go to sleep. IF you said "neteiru" I would ask who is sleeping (unless the subject was already discussed)?
nemasu - going to sleep
neteiru - sleeping.
kind of like the "ing" in english
sundeimasu - living
that was used there because its an ongoing action
hope that helps
