They go away. The spell gives you a loan of 5 current HP and 5 max HP, and when the spell ends, you give 5 max HP and 5 current HP back.
(Maybe they intended you to keep the current HP like in other healing spells, but I'd be hard put to reason that the "for the duration" somehow makes the maximum HP temporary, but not the current HP too. We've also little indication this was a mistake, other than it's surprising. So, let's go by what they wrote.)
That can drop you to 0hp, but by the end of the 8 hours, you're probably resting and in a healthy state, and the loss of a portion of your HP won't be devastating.
The fact it can drop you to 0hp might be surprising, but it makes sense from the spell's description:
Your spell bolsters your allies with toughness and resolve.
The spell gives you a little bit of extra oomph to keep you going. (Well, eight hours of oomph.) When the spell goes away, that oomph does too. If you're decently healthy, you'll feel slightly more worn. If you're at 1-4hp, basically on the brink of passing out and dying, then this oomph is the little bit extra that's still keeping you going, and it will be bad if it goes away.
Have healing spells handy if you have someone under Aid, and keep track of time to make sure they're in a healthy state when it ends.
Of course, if you find the above absurd or terrible or something else, you can feel free to say the 5hp granted goes away first, just like temporary HP.
Isn't it Temporary HP?
Probably not. D&D 5e does have rules for Temporary Hit Points, but this spell doesn't appear to grant them. They could have written "temporary HP", but instead they wrote "current HP".
The argument could be made they should be interpreted as Temporary HP because they're temporary, but nothing in either Aid's description nor the writing about Temporary HP really suggests this interpretation should be made. Aid seems to grant real HP, which means it can do things Temporary HP can't do, like bring you back from 0hp.
Reduction in maximum hit points (max HP) is essentially 5e's replacement for the energy drains, level drains and negative levels of earlier editions.1 As such, it is not meant to be easily or quickly overcome, so low-level magic does not work. In fact, the 5e demilich's legendary action is called "energy drain" while many undead in 5e (specters, wights, wraiths) have a "life drain" effect similar to the vampire's bite. However, max HP reduction is not exclusive to vampires or the undead in 5e. Players can temporarily cause the same effect with the 6th-level Harm spell and other monsters have similar attacks that do not involve necrotic damage. The other max HP reducing attacks and their respective cures are:
- blue slaad's claw – unclear (involves disease), but maybe only a wish spell (MM, p. 276)
- chasme's proboscis attack – long rest or spell like greater restoration (MM, p. 57)
- clay golem's slam attack – greater restoration spell or similar magic (MM, p. 168)
- demilich's energy drain – greater restoration spell or similar magic (MM, p. 48)
- mummy's and mummy lord's rotting fist attack – remove curse spell or other magic (MM, pp. 228-229)
- night hag's nightmare haunting – greater restoration spell or similar magic (MM, p. 178)
- otyugh's bite – daily saving throw (involves disease) (MM, p. 248)
- succubus'/incubus' draining kiss – long rest (MM, p. 285)
As listed above, the means of restoring max HP are specified in the description of the ability/effect that causes the reduction to max HP. This is almost always powerful magic (i.e., the 5th-level "greater restoration spell or similar magic") or a long rest, the latter particularly for undead (specter, vampire, wight, wraith). However, a DM can interpret "similar magic" or house rule other powerful magic that can immediately restore max HP. For example, the blue slaad's claw and otyugh's bite create diseases that cause max HP reduction, so the 6th-level spell Heal may work since it "ends ... any diseases." Similarly, Heal washes its target in positive energy, so a DM could rule that it restores max HP to characters affected by the "life drain" of undead.
- The energy drain mechanic in AD&D 2e was the loss of entire levels and everything that had come with each (e.g., HP, proficiencies, skills, spells, etc.) while 3e imposed a -1 penalty on all skill and ability checks, attack rolls, and saving throws, -1 prepared spell and spell slot and -5 max HP (-1 HD). There is an EN World forum thread that anecdotally discusses the psychological impact of level and max HP reduction on players.
Why describe the damage?
I've played and GM'd in a few editions of D&D and while it certainly seems to be a table preference, I've never seen the value in breaking the flow of combat to narrate every single to-hit die roll on a spell or attack based on how much it met or failed the DC and how much damage the player happened to roll. The damage is already described numerically by the player. My personal experience as both GM and Player has been that this feels like it might add more narrative to a fight but there's a finite number of ways each person can describe most of the standard situations. Its inevitable that certain speech patterns will be repeated.
Only narrate major changes
It's been my experience as GM and player in D&D that only signaling bloodied (half hp threshold passed) and death in a narrative flourish is worthwhile. On tough enemies signifying to players that they are halfway there can be a relief and a good moment to spice up the combat with a bold description. Examples like "the dragon's scales are cracked" or " the knight sways on his feet" can be simple, characterizing ways to signal the half HP threshold has been passed and if you are only telling players hit/miss normally the very fact you narrated to begin with signals the import. (4e treated this as an actual mechanical condition "bloodied" and 5e treats it more of a descriptive threshold but there are some class features or monster features that function off of the half hp threshold).
Likewise enemy deaths are a perfect momement to narrate and the length and granduer of the narration should scale with the enemy. Did they just manage to kill a vampire within their lair? Ham it up, make it as dramatic as possible. Was it a monster they've fought before as a danger in a dungeon room, not part of a greater storyline? Keep it prefunctory and short to keep the adventure flowing.