Alright you've got a standard group of 4 (or 5) adventurers that head into the goblin's cave to slaughter teh evils. Or whatever.
Now in our storybook ideal world, they go in and with a single blast of magic or blow of a sword, the goblins fall to them...except for these 2 or 3 elite goblins that are in charge of the raiding party. These goblins are able to dodge blows that would normally have slain them, taking only grazing hits while ordering the weaklings to swarm the enemy.
In gaming terms that translates into the idea that you have some creatures that a single hit is just a death blow. It's not so much that they only have 1 hp, it's more that unlike other units, they aren't able to dodge a successful hit and turn it from lethal to wound. Other non-minions are able to dodge blows that would normally kill a goblin and thus are able to put up more of a fight.
At higher levels, you have the same group of adventurers that are now going up against a group of Ogres. Yes the Ogres mechanically have only 1 hp, but the PCs shouldn't be going up against them until the appropriate time (and if they were to go up against them beforehand because of failure to follow the signs of 'this is a higher level than you're ready for' then you probably want to consider having the minions hang back to prevent the PCs from believing they are stronger than they really are) making the entire story still work.