A rule for assigning to each point of a general space or spacetime a set of numbers for purposes of identification.
Many readers will know two examples from school: In the case of the line of real numbers, every point on the line corresponds to a real number which can be seen as its coordinate. What’s important is that these coordinates reflect neighbourly relations: The number 1 lies between the number 0 and the number 2, and so does the point corresponding to it lie between the two points corresponding to 0 and 2. The second example is the usual X-Y-coordinate system (sometimes called Cartesian coordinates), by which every point in a plane can be characterized by two numbers: the first its X coordinate value, the second its Y coordinate value.
The examples reflect an important property of coordinates: To uniquely identify a point in space, one needs as many coordinate values as the space has dimensions.
Of the four coordinates defining an event in spacetime, three serve to fix its location in three-dimensional space, while the fourth gives the point in time for the event.