5v relay to a 3v DC motor

I have an Arduino Uno and a 5V one channel relay module. I just realized that I have a few 1.5-3v DC motors laying around and was wondering if I could connect all of them together.

I was reading up on the relay module and my understanding is that it connects and disconnects the circuit. I'm curious where the 5v comes into play. Is it just for connecting it to the Arduino's 5v pin?

Would it be alright if I have my 5v relay module connected to the 5v pin, ground, and a digital pin of the Uno. Then I would connect my motor to 2 AA batteries and connect that to the relay. Would that be fine or would there not be enough energy since the relay is looking for 5v?

If I understand your description, yes.
But to be certain I would want to see a schematic.

The best thing is to post your proposed schematic, not a frizzy thing. Be sure to include all power source, power, ground, interconnections, and links to the hardware devices. According to the description of the relay you can do what you want I think as you are not very clear. Remember an Arduino a Power Supply it is NOT! Probably the best thing you can do is spend some time going through several tutorials on basic electronics and Arduinos. The Arduino Cookbook is a great reference, try to borrow one from your local library.

Is it just for connecting it to the Arduino's 5v pin?

In this case (single relay) yes ... 5VDC is used to power the relay module.
The relay contacts (switch) is rated for switching a load of up to 10A at 28VDC maximum.