What it is:
An easement is a legal right to trespass.
How it works/Example:
Let's say John Doe owns five acres of land. He retires and decides that he doesn't want to keep paying property taxes on the full parcel. He decides to sell two of the five acres to Jane Smith, who builds a house on the parcel.
Because the land is surrounded on three sides by rivers and forest, Jane must drive over a patch of John's property to get to her house. When she buys the land, she negotiates an easement (probably at an extra cost), which allows her to have a driveway from the main road, over John's property, and to her house.
Utility companies often have easements on property so they can access utility lines, sewer pipes, cables and other physical components. In most cases, the easements dictate what sort of activity can occur (i.e., only for driving, not building).
Why it matters:
Easements often can be negotiated, and often they accompany the deed to a piece of property (so that the users of an easement don't lose access if the property sells). Sometimes, easements become implied if the same parties use a portion of a property for a long period of time.