Is an idiomatic Verb-Particle combination (VP). That is, it doesn´t have a parsing value, so they are studied as a unit.
With the verb we know it´s a verb but the other word doesn´t have a defined function.
Other Idiom particles usually have some semi-defined roles (up-off, etc) but with OUT it´s different, with any given example it changes, the particle "out" I mean.
In this case "out" seems like having something of an "away" role, or "something that goes outwards from me, from my property" (but here it´s my guess, a personal point of view).
"Rent out" means that you rent something (property) to others, that you bought something to the purpose of renting, making money from it (most of the times it´s like this, as in "Rent-a-Cars" example). Sometimes it has to do with earning an extra money for something (a rent of opportunity).
In your sentences, say, if I have an apartment and I go to another city for a time I may "rent it to my nieces". Whereas, if I am have some apartments for rent, my nieces can choose one from the set, and I rent it out to them.
Anyway, in this case there´s some intersection in meaning, and you see people using one way and the other to describe both situations.
And there´s another meaning to it as well, "rent it out" could also mean "sublease it" (a "re-rent" meaning here).
They bought the house to rent out to students.
He rents his house out to tourists in the summer.
The field behind my house is mine, but I rent it out to my neighbours and they keep their horse in it.
I am renting out my spare bedroom to get some extra money