What are the applications of binomial trees?
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From wiki's entry
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein (1979). Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument. In general, binomial options pricing models do not have closed-form solutions.
See the full post, http://en.wikipedia.org/wiki/Binomial_options_pricing_model, for methodology/implementation guidelines.
You can also read about Cox-Ross-Rubinstein model (see e.g. Shreve, Stochastic Calculus for Finance I). Binomial trees are discrete-time models assuming that at each step there are only two possibilities for the change of the price.