The toilet doesn't shut off completely. You hear a hissing noise and see ripples in the bowl. This behavior starts intermittently but over time becomes constant.
These symptoms suggest a problem with the fill valve or ballcock. (Remember that all ballcocks are fill valves, but not all fill valves are ballcocks. The term "ballcock" applies only to traditional fill valves, which have ball floats on the end of a pivoting arm.) It may be that you need to remove sediment from the fill-valve diaphragm. Or you may be able to solve the problem by making a simple float adjustment. In most cases, however, the valve needs to be repaired or replaced. Don't put it off. A toilet that won't shut off completely wastes lots of water.
Do the simple things first. If the water level is so high that it spills into the overflow tube before the float ball or cup can shut off the fill valve, adjust the water level. Aim for level about 1 inch below the top of the overflow. With a ballcock assembly, tighten the adjustment screw on top of the fill-valve riser. If that doesn't work, bend the float-ball rod down slightly. Use both hands, and work carefully. Newer fill valves have other float adjustments. For example, a common type has a stainless-steel clip that you use to adjust the height of a float cup. If adjustment doesn't solve the problem, a tiny amount of sediment may be in the diaphragm. See "removing grit from the diaphragm," for how to clean the assembly.
Assuming that the float setting is fine and there is no sediment in the diaphragm, you next option is to replace the diaphragm and float-plunger seals. Begin by shutting off the water and removing the two or three screws that secure the combination diaphragm cover and float-arm assembly to the top of the riser. Lift the cover-and-float-arm assembly from the valve, and pull out the rubber seals. Expect a large rubber disk or stopper. Take these parts with you to a well-stocked plumbing outlet. If you can find replacement seals, install them in reverse order if removal, and test your work. You may be better off replacing the entire fill valve, especially if it's old.