Term: Cone
A Cone shoots out from you in a quarter circle on the grid. When you aim a cone, the first square of that cone must share an edge with your space if you're aiming , as if you are moving at a diagonal. If you're Large or larger, the first square can run along the edge of the space you occupy (or at the nearest squares, if using a grid). You can't aim a cone so that it overlaps your space. The cone extends out for a number of feet, widening as it goes (if using a grid, every single 5 ft square vertically expands the cone 1 square horizontally, or 2 squares total).
As an example, if you cast the Burning Hands spell, you create a cone of flames that originates at the edge of one square of your space and affects a quarter-circle area 15 feet on each edge.
If you make a cone originate elsewhere, use these same rules, with the first square of the cone using an edge or corner of that creature or object's space instead of your own.
For full rules on Areas of Effect, go to Rule: Areas of Effect.