That looks like the internal compenstation capacitor. It creates a single dominant pole over most of the opamp's intended operating range.
Opamps with dominant pole compensation can be characterized by a fixed gain bandwidth product from a bit past the dominant pole frequency and higher. This characteristic can be useful in applications, in particular to allow for circuits with predictable stability without excessive bandwidth loss.
But the opamp can correctly function without the capacitor, correct?
Well, sortof. Compensation keeps it stable in closed loop configurations. It would be much more difficult for circuits using the opamp to guarantee stability if the opamp weren't compensated.
You can account for an overly twitchy opamp in the external circuit to some extent, but that only goes so far. It make more sense for the opamp to at least compensate for its own delay. That compenstation can then be inside the opamp at the optimum place, instead of having to deal the problem externally.
One way to think about dominant-pole compensation is that it handles the stability problems associated with a fixed delay. No amplifier is infinitely fast. There will always be some delay from changing the input until that change appears on the output. Now think about that delay in frequency space. At any one frequency, you can think of it as a phase shift. However, that phase shift gets larger proportional with frequency. Single-pole compensation reduces the gain proportional to frequency so that the net effect of the phase shift on stability remains constant across the operating frequency range.
Many opamps are compensated to the point that they are stable as unity-gain followers. Some opamps are deliberately compensated less to get higher bandwidth. That works if you always want some minimum over-unity gain from them, or the external circuit has to provide its own additional compensation. Such opamps exist, but you need to know what you're doing to use them effectively.