Cross correlation, when two signals are "uncorrelated"?
Cross correlation is a measure of similarity between two signals, where one signal is allowed to be time-shifted. In this sense, the correlation is not a single number, but a function of the time shift. We say, "these two signal have a certain correlation $R(\Delta)$ for a time shift $\Delta$".

Intuitively, two signals that tend to have the same sign (both positive or both negative) for a given time shift $t$ are similar, and will have large correlation (positive or negative). Signals that are uncorrelated are just as likely to have opposing signs, and then the integral will be small.

As an example, consider two signals that are rectangular pulses of duration $T=1$, but one starting at $t=0$ and the other at $t=10$. Their product is zero (and thus their correlation for time shift 0 is also 0). However, intuitively we could say that they are similar, except for the delay. Thus, the correlation allows us to quantify that intuition: these two pulses are completely uncorrelated for some delays; however, when if the first is time-delayed by 10 seconds, then they become highly correlated.

Note that $R(\Delta)=0$ is a sufficient and necessary condition for the two signals to be "uncorrelated" (meaning they have zero correlation) with time shift $\Delta$.