I have this sentence in a report but I don't quiet know what it means. I am familier with covariance and covariance matrices but not with covariance functions.
$f(t)$ is a continuous-time white-noise process with zero mean and the covariance function $\mathbb{E}f(t)f(s)^\top = R \delta(t − s)$.
My guess is is that the $f(t)$ actually has a covariance matrix of $R$, but what is with the $\delta(t - s)$? With $\delta$ being the delta function I guess?
Yes, it's the delta function. The formula means that for every $t$ the variable $f(t)$ has variance $R$ and for every $s\neq t$ variables $f(s)$ and $f(t)$ are uncorrelated. This corresponds to the more intuitve discrete-time white noise.