Given values for a response variable (say, Y) and for certain factors thought to affect the response (say, F1, ... , Fk), a linear model relates the factors to the response using an equation of the general form:
Y = b0 + b1*X1(F1,...,Fk) + b2*X2(F1,...,Fk) + ...
... + bp*Xp(F1,...,Fk) + e
where e is an error or noise term which accounts for variation between Y and the model; and where the model terms X1(), ... , Xp() are certain functions of the factors, defined by the model effects. Note that while this is indeed a model for Y linear in certain variables, it need not be linear in the factors themselves.