The players come around a corner and there's a bunch of goblins about to eat a baby. It's time to fight. Who goes first?
The most realistic way to do it is, of course, everybody rolls individually to see who goes when, or friend and foe both go in dexterity order, or something like that. In the old D&D rules, however, the players roll a die, the dungeon master rolls a die, and the highest side goes first--the whole side.
Obviously this makes things simpler--the DM doesn't have to keep track of the initiative rolls for eight different goblins interleaved with however many players, but I like the one-roll-per-side thing for another reason:
When you play a game, it's chaos. This dwarf guy is fiddling with his miniature, the wizard is checking through her spells, the barbarian is answering a text from her boyfriend, the cleric is worried about being down to one hit point, and the elf is thinking about whether to order pizza--if you've ever DMed you know how it is. You can be describing the most bizarre, epic vista or the goriest critical hit and there's still a chance everybody's off in their own little world.
But then you say "Ok, initiative--the dragon rolled a 4, what about you guys?". Then suddenly everyone at the table looks up, they hand the d6 to somebody--"Ok, you roll it"--and they all gather around this person and get absorbed in that one bouncing die--because if it's a 6 they get to do stuff, and if it's a 3, they get to get eaten by a dragon. And they all would rather do stuff then get eaten.
And in that moment of shared anticipation, they are all a team. The players maybe drove here separately in separate cars, they may drive home separately, they probably made their characters separately and their characters may die separately and from separate causes and they all have separate distractions or worries, and the players may not even know each other, but in that little moment they are all together, and they all realize they are playing a game about teamwork and all relying on each other. And suddenly the wizard cares if the thief can backstab because that'll save him from having to run away and the dwarf cares that the cleric has a healing spell because if he does then he can use it right now and it's all happening at once and they're all paying attention to the same thing at the same time because they are all unified in their fear of impending death.
Which is fun.