Chainsaws are portable power saws. The saw is a "chain" because the teeth are linked to form an endless chain.
The motor of a chainsaw can be powered by gas/petrol or electricity. Gas/petrol chainsaws allow more freedom as they are not attached to an electricity cable. Gas/petrol chainsaws are also more powerful than electric chainsaws but also heavier, higher maintenance and more expensive. A forester's chainsaw is too heavy for most people. The right choice for you will depend on what you want to use the saw for.
Chainsaws are powerful tools and it is imperative that you wear protective safety clothing - particulary a hard hat in case a branch falls on you, leg chaps to protect your legs from the saw should it slip, leather boots with steel toe-caps, gloves with a good grip, protection for your ears from the noise of the saw and goggles to protect your eyes from wood chips. Also avoid loose clothing that might get caught in the chain.