I figure if your teacher hasn't mentioned them, then it's not something you need to fill your head with just yet! It's a sometimes contentious subject that people can get 'wrapped around the axle about.' That being said, there are generally colored belts throughout the first several beginner levels of rank, typically called kyu. Most organizations have their students in the kyu levels from anywhere between five and eight years. Then typically student is awarded a black belt at shodan level. This signifies entry into the 'dan' (pronounced don) ranking system and signifies the student starting their training over, at the beginning, but at a more serious level (it kind of signifies that person is now a serious student of aikido). From there one can advance as a student, which often coincides with increasing teaching responsibility. Most teachers feel instruction is a great way for one to learn about themselves. Some, however, differentiate between training students and teachers and have separate teaching licenses or ranks specific to one's ability to teach, test, and promote.
I am glad to hear your teacher hasn't brought up ranks and testing this early in your training. In my opinion testing and gaining rank should be seen as a fun, and challenging, experience that exists for the sole purpose of providing a fun and challenging experience...vice an activity to serve as a means to an end. Regardless, have fun and enjoy your new training experiences as you receive the fire hose of information coming at you!