Yeah, it's kind of inexplicable, actually. It's perceived as "the present." However, that's in distinction from "the past" and "the future." Both of those, and "now" as well, are abstractions and aren't concrete and are in actuality undefinable.
Actually it's all very definable. But you have to move outside of our understanding of time as it relates to clocks and calendars, and look at time from a definition of light traveling across the interstellar medium.
In as simple an analogy as I can think to present, imagine you are in some far off spaceship, light years from home.
You look through a telescope at home, one with sufficient magical power to see your family on the patio cooking up some burgers.
What you are seeing is in fact their past. It is your present, your "now" but it has happened years ago. You look away to contemplate that.
Now, you look back again and see they have moved. What you previously saw was their past relative to what you have just seen. It's all in the past to them, so let's make another magical leap.
Now you have two telescopes, both are tunneling through wormholes that, for this demonstration, transfer light instantaneously. One is seeing time as everything is happening, like a live video, but one is traveling through a different wormhole that has time dragged down by a few seconds.
Both telescopes relay the feed on a video screen side by side. You see a live video on the right, and the delayed video on the left. You are now witnessing present and past.
I don't know why I made the second part still in space, because you could represent that on Earth easily. Have one video feed that is a true live video, and have another that has the typical delay so they can censor any oopsies. You are witnessing past and present in that scenario just the same.
I hope that helped. Because in reality, there is very much a space-time definition of past and present. Future can be defined just the same, but you get into debates if you try and say the future is concrete. The past and present, however, are very much concrete and are encoded in light for all the universe to see, if one were to set about looking for it.
We see the past every time we look up at the night sky. We cannot see the present of anything in space, we don't have that magical live view. Even when we look at the sun it's 6 minutes old. The sun could be gone, poof, and we wouldn't know it for about 6 minutes!
But if you had super sci-fi magic technology [for now?], you could witness the present and discern the concrete difference between the past and present.