There is a very famous "thought experiment" that comes from Einstein and can be found in countless textbooks, popular science books, and other places (and there are variations of it). For Einstein, it was a thought experiment, but we have long since shown that it is true (and shown in various ways).
Often it involves a spaceship, but as Einstein originally used a train I'll start with that. First, it allows an easier, more intuitive set-up. It's natural to imagine that were you on a train and I standing along the track with my catcher's mitt, what would happen if you threw a ball to me? Imagine that the train you're on is travelling 100mph. You (being the star pitcher you are), throw me your 95mph fastball. From your perspective, it travels at 95mph. For poor me with my mitt, it's travelling 195 mph, because the speed of the train adds to the speed of the ball. This does not happen with light, which leads us to the important example.
Imagine one car of a train in motion along a straight track. A person named Alice is sitting in the middle of that train-car. Another person, Bob, is standing at a single spot along the track the train is travelling on. Naturally, at some point the train will reach Bob, and thus there will be a moment as the train is passing Bob at which Bob and Alice are eye-to-eye, meaning you can draw a straight line from where Alice is sitting to where Bob is standing, and that line will be perpendicular/orthogonal to the track. As Alice is in the middle of the car, naturally she is equidistant from both ends of the car (she is as far from the left end as she is from the right). Although Bob isn't in the train-car, the moment you can draw that perpendicular/orthogonal line from Bob to Alice, Bob is
also as far away from the left side of the train-car as from the right.
All that leads up to the important "event". The moment Bob and Alice are eye-to-eye, lightening (travelling at the speed of light
c, which is constant) strikes both ends of the train-car. We'll call the left side of the train-car A and the right side B. Imagine both Bob and Alice can see both lightening bolts strike. Here's are problem. The light emitted from both bolts reach Bob's eyes at exactly the same moment. So, naturally he asserts that the lighting simultaneously hit both A and B (hit both sides at the exact same time).
Mary, however, sees things differently. Although the speed of light is constant, the speeds at which Bob and Mary are travelling are not. Bob is travelling at the speed the Earth is, but Mary is travelling 100mph faster (how much faster is irrelevant so I picked a number easy to work with). That means as the light waves travel from A and B to Mary, Mary is moving
towards A, and is moving
faster towards A than is Bob. So from her perspective, lightening did not strike A & B simultaneously, but struck B first and then A.
Who is right? They both are. Why does any of this matter? Because it means there is no "now".
Without even leaving special relativity for the much harder questions about space & time we'd have with general relativity (not to mention QM), we now have ways to talk about "events' that differ from what we are used to. I am loathe to get into discussions yet of the contraction and dilation of space and time, but introducing worldlines is important to define
events. Imagine a clock existing in 3D space. It exists in 3D space only as an object without any "now" (any time). To allow time into the picture requires that we say the clock exists in
four dimensional space. We can now think of this clock moving through time. However, it is still defined spatially, and uniquely so. No other clock will experience moving through time the way this clock does. This is true of all things, and we call this movement through spacetime a "worldline" (it's more complicated than this but unless we get into inertial reference frame and uniform motion and other unpleasantly complicated things, we'll leave it be). An event is a point in 4D, and to the extent we can speak of different objects or observers experiencing the same event we do so only through reference to what is called a light cone:
Neither worldlines or reference frames define events; light cones do. The examples above show one reason why: simultaneity for any observer depends upon the "spread" of light waves, which means that we cannot define an event by any frame of reference or the entire wordline of an entities frame of reference.
This creates a problem. An event can occur before another given one reference frame, and after given some other. Light cones allow us to place limits on causality (sort of; we're ignoring problems with nonlocality and the possibility of superluminal signals among other things), but these are "local" and cannot tell us that some event occurred before or after another.