Electric Charge
Electric charge is a basic property of matter that comes in positive and negative forms; like charges repel, opposite charges attract.
Definition
Electric charge is a property some tiny particles have, coming in two kinds, positive and negative, with alike charges pushing each other away and different charges pulling together, and most objects seem to have no charge because they hold equal amounts of positive and negative charge until rubbing knocks the balance off. It is a fundamental property of matter carried by protons (positive) and electrons (negative), measured in coulombs, conserved so it can move between objects but never be created or destroyed, and an object becomes charged by gaining or losing electrons while protons stay locked in the nucleus. Charge is a conserved, quantized, Lorentz-invariant scalar: every free particle carries an integer multiple of the elementary charge $e = 1.602 \times 10^{-19}\ \text{C}$ (confined quarks carry $\pm e/3$ and $\pm 2e/3$), point charges interact through Coulomb's law, $\vec{F} = kq_1q_2\hat{r}/r^2$ with $k = 1/(4\pi\varepsilon_0) = 8.99 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$, and a charge sources an electric field $\vec{E} = \vec{F}/q$ obeying Gauss's law, $\oint \vec{E}\cdot d\vec{A} = Q_{\text{enc}}/\varepsilon_0$, with local charge conservation expressed by the continuity equation $\partial\rho/\partial t + \nabla\cdot\vec{J} = 0$.
Example
Protons in the center of an atom are positive and electrons zipping around them are negative, and that pull holds the atom together; one electron carries $-1.6 \times 10^{-19}\ \text{C}$, so a coulomb is the charge of about $6.25 \times 10^{18}$ electrons, and a balloon rubbed on hair might pick up $10^{11}$ extra electrons, only about $-1.6 \times 10^{-8}\ \text{C}$, yet enough to hold it against a wall. In a hydrogen atom, with the electron about $5.3 \times 10^{-11}\ \text{m}$ from the proton, the Coulomb force is $F \approx 8.2 \times 10^{-8}\ \text{N}$, while gravity between them is about $3.6 \times 10^{-47}\ \text{N}$, weaker by a factor of $10^{39}$.
Key Insight
Charge, not mass, is what electric and magnetic forces act on, so a neutral atom feels no net electric force, which is why electrical forces do not pull a person toward a wall the way gravity pulls toward the floor. The universe is electrically neutral to extraordinary precision; if the charges on protons and electrons differed by even one part in $10^{18}$, electric repulsion between everyday objects would overwhelm gravity, so chemistry, biology, and every contact force exist because charge is balanced so exactly on large scales and so unbalanced on the scale of atoms.