What is time?

Is time a dimension? A process? An illusion? A currency? Does it slow down under the influence of motion or gravity? Do clocks really measure it?

What is time? We know that time is relative. This is not to say that each person has a mentally different experience of time, which is also true, but that at the physical location of person A, regardless of his/her emotional or perceptional experience of time, the speed of time is different from person B if person B is moving relative to person A.  This leads us to the twin paradox:

In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. In fact, the result is not a paradox in the true sense, since it can be resolved within the standard framework of special relativity. The effect has been verified experimentally using measurements of precise clocks flown in airplanes and satellites.

... Both gravitational time dilation and special relativity can be used to explain the Hafele-Keating experiment on time dilation using precise measurements of clocks flown in airplanes. - wiki

To understand time, begin by understanding special relativity:

In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer.

The green dots and red dots in the animation represent spaceships. The ships of the green fleet have no velocity relative to each other, so for the clocks onboard the individual ships the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard fleet time. The ships of the "red fleet" are moving with a velocity of 0.866 of the speed of light with respect to the green fleet.

The blue dots represent pulses of light. One cycle of light-pulses between two green ships takes two seconds of "green time", one second for each leg.

As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of "red time" for each leg. As seen from the perspective of the greens, the red ships' cycle of exchanging light pulses travels a diagonal path that is two light-seconds long. (As seen from the green perspective the reds travel 1.73 () light-seconds of distance for every two seconds of green time.)

One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by ships of the green fleet with two-second intervals as measured in green time. Not shown in the animation is that all aspects of physics are proportionally involved. The light pulses that are emitted by the reds at a particular frequency as measured in red time are received at a lower frequency as measured by the detectors of the green fleet that measure against green time, and vice versa.

The animation cycles between the green perspective and the red perspective, to emphasize the symmetry. As there is no such thing as absolute motion in relativity (as is also the case for Newtonian mechanics), both the green and the red fleet are entitled to consider themselves motionless in their own frame of reference.

Again, it is vital to understand that the results of these interactions and calculations reflect the real state of the ships as it emerges from their situation of relative motion. It is not a mere quirk of the method of measurement or communication. - wiki

Here is time as a currency from timephysics.com

Time becomes evident through motion and is measured by comparison with other motions. Sunrise sunsets, night and day, the changing seasons, the movement of the celestial bodies are all indicative of continuous change.  The aging process is a reminder that molecular  motion and interactions are also at work and are a part of time. Other very important aspect of time is presence of motion of particles like photon and motion at atomic level.

From point of view of physics ... Time is the presence of motion and forces and is caused by the expansion of space.