A continent is generally considered to be a large expanse of contiguous land, ideally on its own tectonic plate. For convenience, we usually group neighbouring islands (especially those on the same tectonic plate) in with the nearest continent.
Traditionally, in English-speaking countries we’ve been taught that there are seven continents:
- North America
- South America
- Australia (or Oceania when you include the wider Pacific Island region)
This division isn’t especially scientific, and has more to do with how historical Europeans (mainly those around the Mediterranean Basin) saw the world. For example, Europe and Asia actually sit on the same continental plate, so scientifically it would make more sense to consider them a single continent, Eurasia, with Europe as a large peninsula dangling off the western edge.
Different cultures divide the continents in different ways. For example, speakers of Spanish and Portuguese usually consider North and South America to constitute a single continent, América. This is even though they sit on different continental plates (in fact, they sit on three: there is a separate Central American plate) and are connected only by a narrow isthmus in Panama – if narrow isthmus connections count, then Africa is also part of the same continent as Europe and Asia, as Africa shares a land border with Asia in Egypt.
We sometimes also talk about subcontinents, particularly the Indian subcontinent, which sits on a different tectonic plate from most of the rest of Asia (the line along which these two plates are converging being the location of the Himalayas). Another candidate for subcontinental status would be the Arabian Peninsula, which also sits on its own tectonic plate.
The continents as they are today are not the continents that Earth has always had. Because the tectonic plates are constantly in motion, different chunks of land have drifted apart or converged together multiple times over in our planet’s history, and will continue to do so for so long as Earth exists. Some prehistoric continents include Pangaea (I believe that one was where all the Earth’s land was joined together) and Gondwana.