Help explain op-amp description by Forrest Mims
There is reference to gain because an opamp is designed to, in the absence of negative feedback, amplify the signal very very large, but vaguely specified amount. This is the so-called "open loop" gain. Open-loop because there is no negative feedback so no loop is closed by a signal going from the output back to the input.

Negative feedback reigns in this very large, vaguely specified output so it is no longer as large as it would have been, but is still at a level larger than the input, and it is now well specified. This is the so-called "closed loop" gain.

We do this because it is difficult to manufacture transistors with accurate and stable gains, but it is easy to manufacture transistors with very very large gains. Then you can use resistor ratios which are easy to manufacture accurately to get the exact gain you want.

The reason a very large, poorly specified gain becomes a smaller, well-specified gain when you add negative feedback is due to the math. The equation for the closed-loop gain (which implies negative feedback) contains resistor values and the open-loop gain as variables. But as the open-loop gain approaches infinite, it approximates itself out of the equation and disappears leaving only resistor values behind.