Scale - Something Other Than What You Weigh Yourself On.
The dictionary defines scale as "the relative size or extent of something" and "a ratio of size in a map, model, drawing, or plan". This a good place to start. In architecture, scale is the size or extent of something in relation to the size of a human being.
So when you hear a person respond to an architectural design by saying "the scale is wrong" what they mean is that the design feels too large or too small. Think Alice in Wonderland.
Scale is a powerful force in experiencing architecture. It's a tool that the architect uses to induce a feeling within a person who is experiencing the architecture. Frank Lloyd Wright was a master at this technique. I remember going on a tour of his home and studio, Taliesin, in Wisconsin one summer and was amazed at how open a space felt when the ceiling was barely over my head. But because there was a wall of windows along one side and because the other side opened into an adjacent space that had a higher ceiling, the low ceiling space felt all right. In fact, it felt good... cozy and intimate, without being confining.
On the flip side, the scale of the building in the image to the right is very large.
But this grand scale is appropriate here. It conveys to anyone experiencing the space that it is voluminous and lofty, that human beings are small in relationship to the grandeur of this space. This same grand scale would not be appropriate for other uses like, say... the toilet compartment in a master bathroom. I've seen houses with gigantic bathrooms that don't feel cozy or intimate at all. They feel too large. They're out of scale.
When you're working with an architect to design a building or space, the more you can convey your feelings about scale, the better. But if you don't, that's OK because a good architect will figure out your concept of scale just by conversing with you about your project.