Time dilation, as predicted by the Theories of Relativity, is an observed difference of elapsed time between two observers which are moving relative to each other. Say Alex is running very fast with relation to Dana. Alex and Dana will both report back to us that light speed is 186,000 miles per second, and they will both tell us that a beam of light will take the same time from their position to reach point A.
However, Dana will report that Alex's clock is moving very slow, and Alex will report that Dana's clock is moving very fast. Alex will not agree with Dana with regard to the distance from her to point A, and vice versa. To Dana, not only does Alex appear to be moving slowly, but his distance measurements are shorter than hers due to length contraction. Dana and Alex will not always agree on the order of events, so that the relative past and future will not be the same (Relativity of simultaneity).
It is important to tell yourself again that for each observer, the speed of light, time measurement, and distance calculation (amount of space between points) remains the same. So if there were a continuous change to our relative time position, our perception of time would remain consistent, and it would not be noticeable.
