A pest is something that competes with us for food or affects our lives in some bad way such as when woodworm gets into our houses. It doesn't know about us - it just does its own thing. But when it eats or destroys our food, that is a serious threat. Pests world-wide reduce the food for humans by up to a third, so it is no small matter. Rats carry disease, rabbits eat grass that was meant for cattle, mosquitoes carry disease, and so on.
As you can see, some pests are large, others small. The most important pests are insects and mites, followed by worms, slugs and snails. Some pests are quite large, like rats. They are mammals. Birds can also be pests in large numbers.
We tend only to think of these other living things as pests when they occur in large numbers. Some crops can be ruined by them, such as Colorado potato beetle and boll weevil on cotton plants.
Plants can also be a pest if they stop crops growing. Plant pests are called weeds.