They're basically the same as the Emotional/Needs potions you can buy in the Aspiration Rewards Shop thingy.
But with two side effects:
1) Your skills level up faster while the effect lasts (4 hours)
2) You have a chance of "withdrawal" when the effect expires, giving a +2 Uncomfortable moodlet for a few hours that makes you learn slower until it goes away (8 hours, I think). Withdrawal doesn't always happen, but can also be ended early by drinking more Celebuserum
You can't actually become dependent on it, and the +2 Uncomfortable moodlet is the only bad side effect
Each celebrity in the house who has that perk will receive a random potion in the mail every day.
Potions come in these varieties:
Confident (+100 Confident)
Flirty (+100 Flirty)
Happy (+100 Happy)
Focused (+100 Focused)
Inspired (+100 Inspired)
Energy (+100 Energized)
Sleep (fills Energy need, +5 Happy)
Fun (fills Fun need, +5 Happy)
Hygienic (fills Hygiene need, +5 Happy)