A cap between the inverting input and the output acts as a low impedance feedback for high frequency content - as the frequency content of the signal goes up, the impedance of a capacitor goes down (provided you're not past its lowest impedance point), so more of the signal is let through to the input to cancel it out. This is useful if, for example, you want some low pass filtering on the signal coming in, as the higher frequency content on the input is reduced on the output because the feedback path is less impedance than just the feedback resistor.
I woudln't expect this to cause ringing, though, so maybe there's something else going on? Are you actually seeing ringing on high frequency edges, or are you just seeing oscillation on the output? With the same consideration... what are your frequencies/waveforms like and how is your probing? If you're seeing inductive ringing on signals that are a few MHz, it could easily be that your probes are ringing and the circuit is fine. If it's actually ringing from the opamp, reducing the gain or increasing the value of the feedback capacitor (increasing high frequency rolloff) could help. If it's oscillations from the circuit, you can try to reduce capacitive loading of the output, or if the amp is driving a high impedance, you could add a load resistor on the output. Additionally, as a general guideline for ringing issues, decreasing trace/wire/lead length on the components used will help by reducing stray inductance.