A suit of five cards, normally headed by at least two of the top honours (ace, king, queen). Any six-card or longer suit. Bidding a suit twice or overcalling in it at the two level or higher normally shows a rebiddable suit.
With the first hand, you do not have a rebiddable suit. You open 1NT (weak) or, if RHO opens 1♠, you double. With the second hand, you do. You open 1♣ or, if RHO opens 1♠ (or a red suit), you overcall 2♣.