Cross validation

Suppose we are training a model on some training data $T$. If we partition $T$ into folds $T_i$ for $1 \leq i \leq k$. Then cross validation is the practice of training the model on all but one fold $T_j$ then assessing it on $T_j$ using our objective function. The practice usually involves doing this for all possible folds and picking the model with least error.