Definitions of biological control (biocontrol, for short) vary, but biocontrol could be broadly defined as:
using beneficial organisms to reduce populations of pest organisms, or to maintain them at sufficiently low levels.
Either the pest or beneficial organism might be a vertebrate (e.g., rodents), an invertebrate (e.g., insects, ticks, slugs), or a microorganism (e.g., fungi or bacteria). Aphids and ladybugs are an example you might be familiar with. Ladybugs eat the aphids that might otherwise damage plants.
But biocontrol is not limited to releasing beneficial insects like ladybugs. Some bacteria and fungi produce compounds that are toxic to pests, including insects, bacteria and fungi. Others protect plants from pest microorganisms by growing on the plant surface, leaving no room for the pest. Some nematodes (microscopic worms) invade and kill pest insects that live in the soil.
Often the beneficial organisms that might feed on pests are already nearby (e.g., bats that eat insects or ladybugs that eat aphids). By improving and protecting their habitat, we can also improve pest control.