FBOs offer an array of services to pilots and aircraft owners. Fuel is usually at the top of the list, followed by aircraft maintenance, aircraft rental, and pilot supplies like sectional charts. With any luck, there will at least be coffee, a vending machine or two, and a restroom. Larger facilities frequently have pilot's lounges with telephones or computerized weather and flight planning services, or even showers and "snooze rooms." They may offer you a place to park your airplane or hangar it overnight (for a fee). Some may charge you a landing fee as well, although this money goes to the airport owner. Many flight schools are actually FBOs that offer flight instruction along with avgas, rentals, and the like.
You can find out whether your planned destination has an FBO by checking the Airport Facility/Directory or AOPA's Airport Directory Online. If the basic airport symbol on your sectional chart has small protrusions - ticks - around it, then basic services or fuel is available during regular working hours.
Some FBOs prefer to handle larger commercial aircraft, and if there is more than one FBO at your destination, you'll want the one that is small-airplane friendly. Call ahead, or contact the FBO on its ARINC frequency - if it has one - to keep the unicom or CTAF free of requests for top-offs and parking directions.