Parzen density estimation

Question

Given a collection of data points $(x_1, ..., x_n)$, we assume they are drawn from some distribution with known parameters (say normal). Parzen density estimate is defined as $p(x) = (1/(nh))*\sum_{i=1}^n N((x-x_i)/h)$ ( or whatever function K from which the data points are drawn). I am having hard time interpreting this. The graph of the density estimate looks like a combination of many normal distributions, each connected to its neighbours. How to calculate this function of all other normal distributions? Also, what exactly does this formula output? The probability of a new point x happening? Isn't this a continuous case, so the probability at a single point should be 0? $n$ is the number of data points and $h$ is a parameter which specifies how "wide" the kernel function should look ( for example, if it is uniform distribution, it will just be the width of the rectangle ). I would also appreciate any good remarks and clarifications on Parzen density estimation at all, because I am not entirely sure that I get the idea of it. Thank you.