Cov(X,Y) = E[XY] - E[X]E[Y]. Positive when they tend to move together, negative when opposed.
The trap. Its magnitude is uninterpretable because it depends on units - covariance in dollars-times-shares means nothing on its own. That is why correlation normalises it.
Why it matters. Portfolio variance is w'Σw, so the covariance terms are where diversification lives. With n assets there are n(n-1)/2 covariances to estimate, which for 100 assets is 4,950 - far more parameters than short histories can support, which is why shrinkage estimators exist.