When an entire group of living things is killed, that's extermination. If ants have taken over your entire kitchen, marching across the counter and up the sides of the cabinets, you might have to resort to extermination.
If you smack just one mosquito, it's not extermination — a whole group must be destroyed in order to call it extermination. Spraying pesticides on your lawn to eradicate every dandelion is extermination, but if you do that you might be contributing to the inadvertent extermination of honey bees too. This destructive noun comes from the Latin exterminare, "drive out, expel, or destroy."