According to the 2013 Notting Hill Carnival's FAQ, "Sunday is Children’s day and Monday is Adults day."
Can anyone please describe the difference between the children's and adults' days?
Historically there's been a reasonable amount of violence associated wit the carnival, for various reasons. For this reason there's usually a large police presence, and presumably why there's a different day for families, but that's a presumption.
Also associated with the carnival is an amount of drugs. You WILL smell marijuana, and may even get offered stuff. You can certainly find it if you wanted it.
However, I've only gone on the 'adult' day (three times), and each time has been a fun day in the sun, with the floats, parades, music, delicious food (mmm...jerk chicken) and happy people.
Also found out that on "Kids’ Day, ... the costume prizes are awarded. On Bank Holiday Monday, the main parade takes place." — http://www.thenottinghillcarnival.com/about/