Given am observed collection of n $\in Z^+$ random variables at arbitrary time points $ t_1,t_2,...,t_n$, a time series is defined by the joint distribution function $$F_{t_1,t_2,...,t_n}(c_1, c_2,...,c_n) = P(x_{t_1}\le c_1,x_{t_2}\le c_2,...,x_{t_n}\le c_n) $$
The text then goes on to define the marginal distribution functions to be $$F_t(x) = P\{x_t\le x \}$$
and the corresponding marginal density functions as $$f_t(x) = \frac{\partial F_t(x)}{\partial x} $$
Can someone please explain the intuition behind the marginal distribution function(s) and the marginal density function(s) and perhaps provide some sort of a brief derivation of the relationship between the two? The notation is tripping me up.