Again, this model of a line is really not very good, but until we learn how to draw a line with 0 width and infinite length, it'll have to do. A plane has two dimensions - length and width, no depth. It's an absolutely flat tabletop extending out both ways to infinity. Space, a huge empty box, has three dimensions, length, width, and depth, extending to infinity in all three directions. Besides its size, it's just a hexagon drawn to fool you into thinking it's a box.
Fractals can have fractional dimension.
A fractal might have dimension of 1.6 or 2.4. Again this isn't a great picture of a fractal. It's really just an approximation of one. Fractals really are formed by infinitely many steps, not just the three of this one. In order to see how fractals could have dimension of a fraction, let's see what we mean by dimension in general.