Time is, like length, a dimension of extent. That is, objects occupy bits of space and occupy time. In practice, they occupy bits of space over a bit of time, or in total, a bit of space-time. Like space, time gives a coordinate for objects to occupy: eg 'he was there yesterday' gives a space-time coordinate.
One can readily get around the question of 'fourth dimension', by realising that one can use 0 as a dimension coordinate, and use that for the temporal coordinate. For the linear dimensions, gravity and motion provide the first two coordinates, which after there are variations of 'across'.
Of space-time itself: this is just a graph. You can make an animation by putting down layers of x,y,z at t0, t1, t2, t3, .... Cartoons work like that. Galilean space-time has no conversion between space and time, because no velocity is absolute.
Electromagnetism provides that waves travel at a fixed velocity, and by galilean laws one could measure this against the 'etherfer'. Experiments by Michelson and Morsey failed to show this. This means that in order to keep this relative, one must allow a conversion between space and time (that, eg different observers travelling at different velocities, should see each others frames different to their own). In order to preserve momentum, energy and the velocity of light, one has to implement something like relativity. Likewise, to keep these relative to gravity, one has to implement a co-gravitional force, which behaves like magnetism.
Still, for the greatest part, these forces and effects are so faint that we choose to dismiss them out of hand.
Mass and charge are dimensions of quantity, colour and heat of quality, length and time are dimensions of extent.
When one reckons the dimensions, the proper order is 0 = time, 1 = height (gravity), 2 = forward (motion), 3 = width (across), 4 = width (across) &c. One normally counts to ignore 0 (ie space alone), or 0&1 (ie dimensions of the plane are usually forward and left/right, as of the maps.)
The dream you dream alone is only a dream
the dream we dream together is reality.