Of all the measurable quantities, time is probably the most abstract. Yet it is one of the fundamental quantities, like space and mass. The measurment of time would not be possible without periodic events. We measure time as a mapping from a set of periodic events to integers. As for example in Gregorian calendar, we map the event "sunrise on the day Jesus Christ was born on a particular longitude" to the integer 0, and each next sunrise at the same longitude as the successive integer. We then extrapolate this to the prior events as negative integers. Two interesting points are to be noted here. First, we take the biggest set of periodic events which repeat at the same rate and measure time according to their intervals. For example if we have 20 clocks, of them 15 are running at the same rate, then we assume that their intervals are even and the other clocks are "slow" or "fast". But we could as well choose the other 5 clocks as "good" and the rest 15 as "bad" without affecting any measurement.
Another interesting point to be noted is, initially time was mapped from discrete events to integers. Then we started to break them down to "fraction of an event", for example half a day, thereby mapping them to rational numbers. Then we extrapolated in to the extreme, to real number. In physics, when we think of time as a variable, we think of it as a continuos variable of a real number.