This is a bid made following partner’s bid (usually an opening bid but sometimes a conventional enquiry). For example, in the sequence 1♣-Pass-1♥, the 1♥ bid is a response to the 1♣ opening bid. If the response is in the suit partner bid, it is usual to call it a raise rather than a response.
The range for a simple response at the one level is very wide. You can have as few as 5 or 6 points. With a hand unsuitable for a jump shift, you could have 20 or even more points. For a two-level response, the minimum threshold is higher, 9 or 10 points in Acol, but more in some other systems.
With the first hand, you respond 1♥ to 1♦ (or 1♣) but 1NT to 1♠. With the second hand, you respond 1♥ to 1♦ or 2♥ to 1♠.