Something that happens automatically happens in a mechanical way without a person having to do anything extra. If you walk through a door that swings open by itself, it opened automatically.
When something is done automatically, it does it on its own, like a spellchecker that corrects your spelling automatically. In a crash, a car's airbag automatically fills with air. Many computers automatically go into rest mode (to save energy) if you don't touch them for a few seconds. Automatically can also refer to how you do something without thinking about it, like if you automatically walk into your old apartment and startle the new tenants.