Can someone explain to me scalar fields?

Question

I would like to gain a deeper understanding on scalar fields, especially those which are derived out of vectors. Take for an example a multi-variabled scalar function. The function itself would be a scalar field; however, it is derived from a vector, say $x = \langle x_1, x_2, x_3, \cdots, x_n\rangle$. How would such a field look like? How would you plot such a field?