Lets start with explaining why the statement "time is a dimension" is a silly thing to say. We're familiar with 3 spacial dimensions. Generally we can move freely through them. By turning left onto main street we suddenly go from a north/south direction to an east/west direction. We can also adjust our speed by applying the break or hitting the gas. Finally (and this is a little less obvious) the more we travel in one spacial dimension the less we travel in another.

To explain this last part, let's say we're traveling in a car going exactly north at 100 kph. Lets say we turn to the north-west but keep our speed constant. We're now traveling to the north at about 71 kph and to the west at 71 kph. If we take those two components together (using the Pythagorean theorem) we find we're traveling to the north-west at (about) 100 kph.

If we turn completely to the west, we're now traveling at an overall speed of 100 kph, to the west at 100 kph and we've completely stopped traveling to the north.

Right, so time isn't like the above at all. Namely, we can't freely travel forward and backwards through time, we can't adjust our speed through time and traveling faster in spacial directions doesn't rob us of our speed in some confusing "time" direction. On an intuitive level, time is nothing like spacial dimensions.

Unfortunately, in the 20th century Albert Einstein came along and took a bit steaming shit on our intuition and he called it "special relativity".

It turns out (this may sound like a hand wave, but humanity has done lots and lots of experiments to directly observe the following weirdness) we can adjust our "speed" through time and traveling in any spacial direction robs us of our speed through that time direction. Unfortunately we can't travel freely backwards through time... but objects that do travel backwards through time have been predicted and the properties of these objects don't directly contradict anything we've observed.

I can't go into the specifics of special relativity or exactly why special relativity is true. However I can say that special relativity is the most accurate set of rules we've been able to come up with to explain the world around us.

In summary, the faster you move through the normal spacial directions, the slower you move through the time direction. When you are completely stopped you speed along through time at a rate of 1 seconds per second (you read that right). When you travel at near the speed of light (a cosmic speed limit) you travel through time at nearly 0 seconds per seconds (again, you read that right). To put that another way: Some person not speeding along will observe you moving very fast and see that your clocks are ticking very very slow.

Spacial directions and time are so similar that treating them both as spacetime makes reasoning about the universe a whole lot easier.