Field Concept #1

Coulomb's law says:

$$F = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{Q_t . Q_s}{{r_{st}}^2}$$

Just consider the test charge as unity. We are left with,

$$F = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{ Q_s}{{r_{st}}^2}$$

Making a slight change in notation ( replacing F with E ) we get, 

$$E = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{ Q_s}{{r_{st}}^2}$$

Conclusion: Mathematically speaking, this is what we call definition of  "Electric field".