“Everything is always moving at the speed of light through spacetime” <— this is so hard to wrap my head around.

“I can understand why it's confusing. For starters, the notion of "speed through spacetime" seems ill-defined since you're using time as one of the "distance" dimensions, but you need a "time" dimension to do a "speed = distance/time" calculation. Really, that's why it's a constant: there's no "meta-time" against which to measure the velocity of our motion through spacetime. So it may be more correct to say we define our necessarily-constant "speed through spacetime" as c. Or rather, we define it as 1; c is just a conversion factor to deal with the fact that we perceive space and time so differently.

Let's back up. Whenever you're moving, you have a velocity. In physics, "velocity" is not just a fancier word for "speed"; it's technically a different value, because it includes direction, making it what we call a "vector quantity". Your speed may be 88 miles per hour, but your velocity is 88 miles per hour heading northeast.

Speed is therefore the magnitude of the velocity; it's the value with the direction taken out. Velocity is commonly expressed this way, as a speed + a compass heading or similar angle, and represented graphically by an arrow on a map pointing in the direction of travel with a length proportional to the speed. But the other common mathematical representation is as a combination of speeds measured in two perpendicular directions - say, north and east – which are called the components of the vector. Traveling 88 mph due northeast (that is, on a heading of 045º) is the same velocity as (44√2̅ mph N, 44√2̅ mph E) – where 44√2̅ works out to about 62.

Either way you need two numbers, but the component representation is more useful mathematically. Mostly that's because it can be treated like a number in many important ways: it can be multiplied or divided by a scale factor just by doing that to each of the components, for example. Or two vectors can be added together (say, to determine the impact of an incoming wind on an already-moving sailboat) just by adding their corresponding components. Stuff like that. (Though in our relativistic universe velocities don't strictly add; that's a great approximation down here at extremely sublight speeds, but in reality there's a scale factor that keeps the sum from ever getting as high as c.)

Both representations easily extend to three dimensions - you just need a third number (an elevation angle or vertical velocity component) to account for rising/falling speed. But our universe isn't three-dimensional; it's four-dimensional, with the fourth dimension being time. Our brains aren't equipped to visualize four perpendicular directions, so while we can derive a set of angles for measuring direction in 4D, they kind of lose their point. But adding a fourth component to a vector is easy.
Still, the component representation only makes sense if all the components have the same units, and we don't measure time the same way we measure distance. To make sense of this it helps to understand c as the conversion factor between space units and time units. If relativity shows us that space and time are made of the same stuff - spacetime - then c tells us how they relate: one light-second of space is the same amount of spacetime as one second of time. Which from a human standpoint seems like an awful lot of space equating to not very much time at all.

The other salient point about time, or at least the way we perceive it, is that we're always moving forward through it, at a constant rate of 1 (second per second, minute per minute, pick your units; they cancel out). But the conversion factor means that rate is also c. Every second of your life you move the equivalent of 186000 miles/300000 km through spacetime. It's just that almost all of that motion – all of it, in your own reference frame in which you're not moving through space – is in the direction of forward time, rather than any of the three spatial dimensions. (Which is interesting to think about philosophically; if the universe of just one second ago is already 300,000 kilometers away, the past isn't just another country, it's another planet! But we're not talking about philosophy. :) )

To go back to two dimensions, imagine you started out going due north, still at 88 mph. Your velocity vector components at that point would be (88mph N, 0) - you aren't moving east or west at all. If you then turn just a little bit east without changing speed, then the northward component of your velocity will decrease to make up for the increase in the eastward one. For example, if you turn to heading 007º, your velocity will change to approximately (87 mph N, 11 mph E).

This is a way to think about time dilation; moving through space means you have to slow down your rate of travel through time to keep the same overall velocity through spacetime. And the faster you move through space, the slower you move through time.

If you could move through space at c, like a photon does, then you would stop moving through time altogether, which matches the relativistic conclusion that a photon doesn't experience time. In our analogy that's like turning due east; no northward motion at all.” —- u/zeekar