The extreme case, in which electrons spend all of their time near one of the atoms, is called an ionic bond.
These bonds occur when one atom "wants" to get rid of an electron and another "wants" to gain one. In the example of NaCl, Na "wants" to get rid of an electron and the sodium wants one and the electron goes permantly "near" the Cl, leaving the cloride negative, because it has one extra, and the Na positive, because it has one less.
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