An Island is an area of land surrounded on all sides by Water. Islands can be in Oceans, Seas, Lakes and rivers. Islands surrounded by sea or oceans tend to have temperate climates because the seawater prevents temperatures becoming extreme.
Island or continent
Islands are smaller than Continents, Australia or Antarctica are the smallest continents and Greenland is the largest island. So every land mass larger than Greenland is a continent and anything smaller than Antarctica or Australia is an island.
Typically islands are Geologically different from continents, some are Volcanic islands and others are part of a nearby continental land mass. Still size is important in defining an island. If a small piece of continental crust separate from any continent is found in an ocean will we call it a continent or an island?
Many factors determine what is an island and what is a continent.
- Tectonic separation from continents/other continents
- Unique Plants and Animals
- Unique culture
- Locals see themselves as a continent or an island
The above definitions make Greenland an island while Australia is a continent. 
If we ever discover intermediate land masses on Exoplanets we'll need better definitions.