Ripley's K(r) is a second-order statistic for assessing clustering of a point process at multiple distances (r). It is more exploratory in nature and can be used to understand the spatial structure of your data or to specify other models. In essence it provides a series of global coefficients using a comparison of the observed clustering compared to an expected CSR (complete spatial random) process at variable distance lags (bandwidths) and does not provide an estimated value at the observation. Customarily, you plot the K(r) against the distance lags (r). It is a very robust point pattern statistic not only because it is multi-scale but also because it does not assume stationary and is not subject to anisotropic effects (directional autocorrelation). I should note that the K(r) is unitless and as a result is often transformed to the Besag's L function (Besag 1977). This transformation is quite simple L(d) = sqrt( [K(r) / pi] - r) where r a vector of bandwidths. This linearizes the K(r) and standardizes it around 0. It is quite important to significance test the results, which is often done via Monte Carlo simulation.
Here are some of the common references.
Besag, J.E. (1977) Comments on Ripley's paper. Journal of the Royal Statistical Society B39:193-195.
Besag, J.E. and P.J., Diggle, (1977) Simple Monte Carlo tests for spatial pattern. Applied Statistics 26, 327-333.
Diggle P.J., (2003). Statistical analysis of spatial point patterns. Edward Arnold London
Ripley, B.D. (1977) Modelling Spatial Patterns. Journal of the Royal Statistical Society B39:172-212.
Ripley, B.D. (1976) The Second-Order Analysis of Stationary Point Processes. Journal of Applied Probability 13:255-266.
