Time remains one of the biggest unexplained mysteries in all of science. It plays a central role in our conscious experience, yet only recently has it taken on a serious position in physics. Prior to relativity it remained merely a parameter, marching forward at one second per second without any explanation as to its real meaning or role in the physical world.
In Relativity we confront the notion that time passes at different rates for different observers. This defies common sense. In fact, it challenges the very core of the core of reality as seen by the human mind.
But what is really significant is the link that the passage of time has with the conscious mind. Consciousness is something that seems to elude physics. The first hint that the conscious mind tied in with physics came with the development of QuantumTheory. But that isn't the whole story. Our conscious experience in life is wholly tied up with the passage of time. For me this serves as a clue to what the universe is really about. Time is physical. Its as physical as you can get. It defines the beginning of life. It defines events that have happened and can't be changed, and it defines the end of life. It does all this with a direct relation to the one thing we know to be ultimately real-conscious experience. That inner conscious life that has eluded science for 2,000 years is the most real thing in the universe. Time is its connection to physics.
What time is physically remains a mystery. Even in subjects like string theory, time is just something passing without any real explanation as to what its really about. This should be a red flag for you. String theory and quantum gravity cannot be "ultimate" theories in any real sense. Time and its relation to the human a (and animal m)mind is more real than any electron of Higgs boson. Yet most physicists just view it as a click on their watch, some sideline data to collect while we measure what is "really" happening. Any final theory will have to really explain time and its relation to the conscious mind.
A good book that is a bit more on the rigorous side is The Direction of Time by Hans Reichenbach. Its not going to tell you what time really is, but it puts time under a scientific lens better than any other book I've seen. More on the popular side is About Time by Paul Davies.
Chances are, the true nature of time won't be explained in our lifetimes. But lets get the conversation started.