ACF and PACF are two functions to evaluate autocorrelation i.e. the correlation between a value and a lagged version of itself.
ACF, Autocorrelation Function shows the direct as well as indirect relation between a value with a lagged version of itself whereas PACF, Partial Autocorrelation Function only shows the direct relationship between a value and a lagged version of itself.
By indirect relation, we refer to all indirect paths through which past data can affect the current day data. For example, how does the value three days ago t-3 affect the value two and one days ago which in turn affects the current value.
Direct relation refers to the direct relationship between the past data and the current value. For example, how the value three days ago is affecting the current value directly removing all intermediate paths.