Homeless people can be a real annoyance in SimCity. Not only do they indicate that there is a problem with your city, but they also start fires, occupy parks and make them less attractive to residents, and generally serve as a nuisance.
You can keep tabs on the number of homeless in your city on the population panel. Homeless people are indicated on the map with a yellow icon of a little person carrying a briefcase. (Why a briefcase? Good question. Maybe it’s a suitcase. Hard to say.)
Homeless Sims are low-wealth Sims who have lost their jobs and run out of money. (Medium-wealth and high-wealth Sims just move out of your town.)
I have read that adding a bus station will help your homeless population go away, because the homeless will take the bus to another town. However, this has not been my personal experience. I had about 380 homeless in a town of about 24,000, and adding a bus station did not change the number of homeless.
The only way to cure homelessness is to make systemic changes to your city. Once you provide jobs (that your Sims can reach in time) or fix your traffic problems, the number of homeless will drop. It is not an instant change: it can take several in-game days for this to happen.
For help on curing homelessness, read this article on the “We need money” and “Out of money” problem.