In three-dimensional space, there is a standard Cartesian coordinate system (x,y,z). Starting with a point which is called the origin (as in two-dimensional Cartesian coordinate system), construct three mutually perpendicular axes, which are called the x-axis, the y-axis, and the z-axis.
Here is one way to imagine these axes. Stand near the corner of a room and look down at the point where the walls meet the floor. Then, the floor and the wall to your left intersect in a line which is the positive x-axis. The floor and the wall to your right intersect in a line which is the positive y-axis. The walls intersect in a vertical line which is the positive z-axis. The negative part of each axis is on the opposite side of the origin, where the axes intersect.
For example, given the above corner-of-room analogy, suppose you start at the corner of the room and move five meters along the x-axis, then turn left and walk four meters into the room. If you are two meters tall, then the top of your head is at the point (5,4,2).