A model is a function F that minimizes error in y_i = F(X_i) + error. Inserting a label simply means a function F(X_i,y_j). Then you optimize it in some way to

A model is a function F that minimizes error in y_i = F(X_i) + error. Inserting a label simply means a function F(X_i,y_j). Then you optimize it in some way to separate true labels from false label, e.g. F(X_i, y_j) = (y_i==y_j)-(y_i!=y_j) + error.