To summarize simply, a chemical bond is the attractive force holding atoms or ions together. Such attractive interaction leads to a more stable state for the whole system comparing to individual atoms.
Valence electrons play a fundamental role in chemical bonding. In the electron configuration of an atom, the outermost shell is called the valence shell, and the electrons in the valence shell (outermost shell) are known as valence electrons. Take the carbon atom for example: the electron configuration of carbon is 1s22s22p2. The outermost shell is the 2nd principal shell, so there are 4 valence electrons in carbon. Valence electrons are the electrons that are the furthest away from the nucleus, and thus experience the least attraction from the nucleus and therefore are most reactive. They play the most important role in chemical bonding.