Trump fit
A major part of the bidding for suit contracts is determining whether or not you and your partner have a trump fit - that is to say, whether your combined holding in a suit proposed as trumps constitutes a fit.
Eight is the number of cards of a suit most widely regarded as indicating a fit.
Seven is not a good enough fit for most purposes because of the very real danger that the split - the distribution of that suit between your opponents - will fall badly against you. (However, if you end up in a seven-card fit with no prospects for a less bad contract, cross your fingers - it quite often doesn't work out too badly.)
Even a fit of eight can be tricky, though the odds of a killer 5-0 or painful 4-1 split against you are nowhere near as bad as in the case of seven. Obviously, a fit of nine or better makes for a nearly-guaranteed smooth ride.
See also: The power of the fit and the split in loser count adjustments.