What are the purposes of the stamps labeled 1 cent and 5 cents?

Before the introduction of the Forever Stamps, stamps had certain values. When the cost of mailing a letter increased, and those old stamps just weren't enough to cover the bill, there had to be a way to make use of the old stamps without just throwing them away, hence the 1 cent and 5 cent stamps.

Example:

Sending a letter cost 32 cents. A 32 cent stamp would cover this expense quite handily.
The Postal Service raises the price of a single letter to 35 cents. Since a 32 cent stamp was no longer adequate, and since using 2 of your previous stamps would be wasteful (64 cents to send a 35 cent letter?), the usage of a 5 cent stamp in conjunction of a 32 cent stamp would be more than adequate to cover the cost and would save the postage user some money.

Of course, now that there are Forever Stamps, that's no longer necessary. Once you purchase a forever stamp, then its value holds (1 letter = 1 stamp).

They can be used with other stamps to reach the exact total required. If you need a second stamp on a first-class letter because it's over the weight limit, it's cheaper to add the correct additional amount, rather than a second first-class stamp.

Postage varies with the weight of the letter. They also allow you to use older stamps when postage goes up. Forever stamps were created to alleviate this problem.