Many people take space for granted. They intuitively see it as an abstract concept. Space is where things are at, or better yet, where things aren't, there's empty space. But that view isn't really accurate. Space is a material entity, it has a fabric, it's made out of particles it interacts with particles.
Dimensions is commonly used to refer to sizes of objects, like a two-by-four piece of lumber refers to it's thickness and width. In science and math, dimensions have a more abstract meaning. They form a grid of coordinates for an object to be at. They are intuitively often approached as grades of freedom. For example, inside a dot you are completely trapped and cannot move anywhere. On a line however you are free over one dimension since you can go left to right and vice versa. On a plane one can move both horizontally as vertically, so on is free over two dimensions and so on...
However, next to this intuitive view, there's an alternative way to look at it. You could say that when being confined in a first dimension one can still roam a plane freely while being confined in a first and a second dimension, one can only move along a line. Rather then seeing dimensions as levels of freedom, they become grades of restriction. Although both views are quite similar, the difference is that in one view absolute freedom is acquired by gaining freedom inside all existing dimensions; while in the other freedom is all about being ungrounded (outside) off all dimensions in the first place.
Although this might seem insignificant in our day to day lives, in philosophy this can have far-stretching results. Some arguments against the existence of God rely on this intuitive approach of dimensions for example. (More about this here)
In physics, according to the "standard model of particles physics", all elemental particles can be sorted into either "fermions" and "bosons". [These fermions are all the particles associated with matter and objects, bosons are all messenger particles which cause the four known forces of nature (gravity, electromagnetic force, strong force and weak force).]
Now, interestingly the standard model has a strange view of what these fermions are made out of. First of all, each type of fermion comes in two flavours: matter and antimatter. Secondly both seem to cancel out each other's existence! The standard model explains this, by proposing that both the matter and antimatter particle are made up by the same raw particle. And by proposing that the characteristics of these raw particles change depending on which space they're at. According to the theory, space is like a big checkers board, with empty boxes. Some of them by nature have a negative charge, and some of them have a positive charge. Now if we insert a raw particles, in all off the negative boxes, and leave all the positive boxes empty, the end result would be empty space; a vacuum. If however a particle ends up in a positive box, then we will be able to perceive that particle as matter. Likewise, if we leave a negative box unfilled, that will show up as antimatter. This is why matter cancels out it's corresponding antimatter. The extra raw particle fills up the empty box. This strongly favours the alternative views on dimensions, where dimensions are grades of restrictions rather then grades of freedom. Space is a container. A particle bound to the container is thus limited to it's 3 dimensions.