While your dryer does make some noise during normal function, that noise should never be squeaking. Even small squeaks that you can ignore should not be ignored because they are a symptom of a problem. However, as to what problem they indicate, there can be a few.
Does your dryer squeak with the rhythm of the drum turning? Then it is likely the dryer belt that is responsible. Over time, the rubber dryer belt that physically turns the drum can become stretched out or worn. The belt can even slip off the pulley. If you have squeaking because of the belt, it is only a matter of time before the drum will not turn at all due to the dryer belt finally breaking.
The pulley is what turns with the belt to turn the drum. Unlike a dryer belt, squeaking caused by the idler pulley will be slightly faster than the rhythm of the cycle as the pulley turns more than the belt does. The good news about this part is that sometimes it just needs a little lubrication instead of replacement.
Does your squeak sound more like a scrape? That is a sure sign that the problem is with the drum bearings. This part is what allows the drum to turn against the body of the dryer with little friction. However, over time, they will wear down and need replaced.
Unfortunately, while they are a small part, drum bearings can be a real pain to replace on your own as they involve removing the heavy drum to do it.
This is the least likely culprit, but if all the other suspects check out, then it is possible that your motor is squeaking. This is often a sort of first warning that the motor is going out. Unfortunately, like the bearings, a replacement of your dryer motor can be complex and will require a lot of time to repair.