When a fixture like a sink, toilet or tub won't drain or drains slowly, there is a blockage somewhere in your plumbing system.
When it's only one fixture, the blockage could be in that fixture's trap and you might be able to repair it yourself by using a plunger or hand auger. (You will often detect a sewer smell when something backs up anywhere in the house.)
If the drain blockage is happening at more than one location, the problem could be in the drain between the fixture and the main line, or branch drain line). Again, after locating the line, you might be able to unclog it yourself with a plunger or hand auger, but in this instance you might be better off calling a professional plumber to clean it out.
If you determine that the problem is in the main waste line and you don't have the equipment, you will probably want to hire a plumber to clear your entire system. (It's a good idea to have this done every few years, anyway.)
If drains or fixtures are clogged in more than one location, it tells a plumber that the leak is probably located in a branch drain line or the main waste line.
If the main drain to the outside from your basement is backing up, the problem is probably somewhere between where your line goes from your house to the main sewer line along your street. Tree roots are a common cause of this problem.