So, dimensions refer to the number of independent directions in which movement is possible. The first three dimensions are the ones we are most familiar with, which are length, width, and height. The fourth dimension is usually considered to be time, with events occurring at different points in time.

Now, when we start talking about the fifth and sixth dimensions, things can get a bit more abstract. One proposal from string theory is that there could be additional compact dimensions beyond the three spatial dimensions and time that we experience directly. These dimensions could be curled up, so small that they aren't noticeable on our scale, or they could be larger and more accessible.

Another concept that involves higher dimensions is fractals. Fractals are complex patterns that repeat themselves at different scales, and they can have fractional dimensions. For example, the coastline of a country may seem to have a two-dimensional shape at first glance, but if we look at it more closely, we can see that it has a lot of intricate details that make it more like a fractal, with a dimensionality between two and three.

So, in summary, while the first four dimensions are the ones we experience directly, there are proposals from string theory and concepts from mathematics like fractals that suggest there could be additional dimensions beyond those we are familiar with.