Electrophiles love electrons, and without them, they become unstable. And to reach a stable state, the electrophiles accept electrons from electron-rich nucleophiles.
Therefore, the electrophiles are electron-deficient species and acceptors of electrons.
A positive charge (+) on an atom of the molecule specifies that the atom is less by two electrons, except for the Hydrogen atom (H), which has one electron that, on losing, becomes H+ (proton).
For example, Carbon can form four bonds with four hydrogen atoms, so the central carbon has eight electrons in CH4. On losing one C-H bond with two electrons, the Carbon becomes an electrophile CH3+.
When the covalent bond has polarity due to the joining atoms’ electronegativity difference, such that the more electronegative atom pulls closer the bond electrons leaving the other deficient, the loss in the electron density of the bond is denoted with the sign δ+, making that atom center electrophilic in nature.
For example, in a bond between carbon and a heteroatom such as halogens, nitrogen, or oxygen, the heteroatoms are more electronegative and will pull the bond electron density rendering the carbon partially positive.
Therefore, the full positive charge (+) indicates complete electron(s) loss to generate a positive ion. And the partial positive charge (δ+) means that the two electrons of the covalent bond moved away to the more electronegative atom causing a shift in the electron density.
A covalent (sigma) bond is formed once the electrophile accepts an electron pair from the nucleophile, an electron-rich group of atoms (shown below as Nu- in red). The electron richness is represented by the negative charge or the lone pair on the donor atom.
Related Reading- Nucleophile, What is Electronegativity (an introduction)