A big dent in a tabletop can be caused by a number of mishaps, though extremely large dings are usually caused by dropping something of significant weight on the table. While it is possible to repair the damage without refinishing or painting the entire tabletop, you're likely to see some uneven coloration on the surface, and will probably be more satisfied with a complete restoration.
Prepare the table for refinishing by cleaning it with a degreasing agent such as dishwashing detergent. Remove any splintered wood from the dent.
Sand down or remove existing paint or varnish using a commercial paint stripping agent. You can use a metal spatula to help remove stubborn layers of varnish or finish.
Heat a shellac stick that’s the same color as your tabletop using an alcohol lamp, Bunsen burner or a hot putty knife. All items can be found at a hardware store, woodworking shop or furniture restoration business. Follow the manufacturer’s heating guidelines for melting the sticks. Work the melted agent into the dent, smoothing it with a metal spatula. Allow the substance to dry.
Sand the entire surface of the tabletop to smooth down the repaired dented area until it is flush with the remainder of the surface. Use your sandpaper to simultaneously remove any other imperfections in the table. Brush off the sawdust with a cloth or dry paintbrush.
Stain or paint the table however you like. When dry, coat with a polyurethane finish to seal and protect the wood.