Understanding churn prediction model
A couple good options would be to look at a Feature/Variable importance plot for your RF model.  Alternatively, depending on the model you could try extracting a couple individual trees from the model and examining them.  However, these methods  wouldn't be definitive; i.e. determining what variables are strong predictors for churn does not mean that they have a causal impact on churn, and an individual tree may be biased and not representative of the aggregation output presented by the RF model. To determine causation, you could use these methods as a starting point to design a test.