Real-time is when events happen at a rate consistent with events in the outside world.
Specifically for game artists, if the game engine renders a scene at a slow rate, the illusion of movement can be lost. To retain an interactive, immersive experience, the engine must react to your input and present you with new updated images immediately. If you are getting smooth feedback, it is real-time. Frames per second is the measurement of how fast the frames are being rendered.
The engine must perform many complex operations, and the effect of that effort is the amount of time needed to draw each frame. By necessity, we must take shortcuts in the image quality to speed up the rendering. However, no single image remains visible for very long. If you carefully choose speedup techniques so that the errors are small, then they will not be noticed during the moment when the picture is visible.