There are three journal articles that detail the core solver technology in ParFlow. Each provides information about a particular aspect, the linear solver, the nonlinear solver and the overland flow component. I've provided DOI links to each reference as well for easy access.
The reference for the linear solver is: Ashby, S.F. and R.D. Falgout (1996). A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations. Nuclear Science and Engineering, 124(1):145-59. (NSE only available online from 1997 on, a report version of this paper may be downloaded here).
The reference for the nonlinear solver is: Jones J.E. and C.S. Woodward (2001), Newton-krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems. Advances in Water Resources, 24:763-774.
The reference for the overland flow boundary condition is: Kollet S.J. and RM Maxwell (2006) Integrated surface-groundwater flow modeling a free-surface overland flow boundary condition in a parallel groundwater flow model. Advances in Water Resources, 29(7): 945-958.
Another paper that is a very nice example an application of ParFlow is: Tompson, A. F. B., Falgout, R. D., Smith, S. G., Bosl, W. J., and Ashby, S. F. (1998), Analysis of subsurface contaminant migration and remediation using high performance computing: Advances in Water Resources, 22(3):203-221.
These references should help provide a theoretical (and applied) basis for how ParFlow works and how it can be applied to subsurface flow problems.
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