# Why does the 'Jacobian of at least one combination of $n$ functions shall be different from zero'?

I've started reading The Variational Principles of Mechanics by Cornelius Lanczos; here is the concerned excerpt from p. 11:

The generalized coordinates $q_1,q_2,\ldots, q_n$ may or may not have a geometrical significance. It is necessary however that the functions $$x_1= f_1(q_1,q_2,\ldots, q_n),\\ .......................\\ .......................\\ z_N= f_{3N}(q_1,q_2,\ldots, q_n).$$ shall be finite, continuous and differentiable, and that the Jacobian of at least one combination of $n$ functions shall be different from zero. These conditions may be violated at certain singular points, which have to excluded from consideration. ...

While I could get that the functions must be 'finite, continuous and differentiable' but couldn't get the condition that the 'Jacobian of at least one combination of $n$ functions shall be different from zero'.

Can anyone tell me what is the necessity of this condition? What does this actually mean? Or why do the functions need to follow this?