A flush is all five cards of the same suit. All hearts, all spades.....
If you can get five of the same suit between your hole cards and the cards on the table, you have a flush. If you can also manage to combine a straight - five cards in sequence - with a flush, that's a straight flush, which beats four of a kind. The only hand that beats a straight flush is a Royal flush, 10 J Q K A of the same suit.
The meaning of the word is 'fullness, abundance'. You'll sometimes hear the expression that somebody is 'flush with cash', meaning they have plenty of it. How, exactly, it came to be used for this particular hand in card games is unknown.
The word flush comes from the Latin 'fluxus', which means flow - which is why you flush a toilet.