Time acts like another dimension so, insomuch as distance being the difference between two spatial points, time is the difference between two temporal ones. So far, so good.
The problem comes when you realise that the speed of light is constant in all frames of reference (whether you're travelling towards it, away from it, perpendicular to it...). Consider a light clock:
I hope you'll agree that that is a perfectly valid form of clock. T = 2L/C.
... but now, consider that light clock on a train. You're on the platform, your friend is on the train with it. Because he is in the same reference frame as the clock, he sees it as shown above. However you see:
The light appears to have travelled further in your reference frame than in his. How can this be? The speed of light is identical for both of you, so it cannot have travelled any further or faster in the same time period. The solution is that space and time are malleable, and so you get
time dilation and
length contraction.
Where:
t' = γt and
L' = L/γ
With γ being:
Where β = v/c.
So it turns out that if you're travelling at the speed of light, v/c becomes 1 and the gamma factor tends to infinity. At this point, all distances become effectively zero and all times become infinite (you effectively stop experiencing time).
[/First Year relativity course]