These chemical bonds are actually called ionic bonds, and they occur between ions. Ions and ionic bonds are really quite simple to understand. Ions are molecules that have small electrical charges. These charges are positive or negative. They repel or attract each other.
Opposite charges attract and similar charges repel.
Table salt, sodium chloride, is an excellent example. Sodium forms positive ions and chlorine makes negative ions. The opposite charges attract each other and make table salt. These charges are identical to those found in batteries or static electricity, but on a much smaller scale. Individual ionic bonds are very weak, but millions of them in combination are quite strong.