It means you don't have to check what dice you need to be rolling for a given test. Its easier basically. You don't have to remember, oh this check is done on d100 or 2d6 etc. Less stuff to remember. Also if you ever what to make a player roll for something not covered by the rules (which i do less and less) there's no debate over what die and what the kind of result you are looking for is.
Easy from one angle, maybe, but more difficult from the angle that usually accounts for more work.
The main issue for me is that in 5e's universal system there are always two variables to consider: What the player has rolled, and what the players needs to roll.
To figure out what the players has rolled you need to remember which ability score "counts", what they're proficient in, and whether they're advantaged or disadvantaged or neither. That is three things you need to know before the player can throw the die/dice and sum it all. But that's only half of it. The ref also needs to determine a "target number" and any adjustments to that (that's another two things to know) before comparing the result to the target and determining a result.
That's a lot of stuff to do a few hundred times in a game !
The old school method is simpler because what the player needs to roll is often fixed. Therefore the only variable is what the player rolls. Moreover, there's very often
no adjustments to what the player rolls.
That is a whole lot simpler and can leave you with a boat load of extra time to get on with your game.
Here's a stupid example for your amusement:
New school d20 system:
I rolled a 13 on my d20, is a 13 enough? You've got +4 for strength, but you're not proficient so your proficiency bonus doesn't count. Oh wait, this is dexterity is it? Okay, so you
are proficient, that's +3, but your ability mod is only +3, so overall you're what... +6? Okay, so 13 +6 is 19. You've got a 19. Is 19 enough? Now we need a target number to compare it to. It's usually 15 on this dungeon level, but this thing is harder than usual, so let's add 5 so you need a 20. Oh wait, you're playing an
elf, which means you're advantaged. Roll another die as well and we'll see...
Old school:
You'll need to throw a d6, go. I got a 4, is that enough? Anyone else would need a 5 or 6, but an
elf needs only 3 or better. You're good.