valence electrons
Not all of an atom's electrons take part in bonding. The inner electrons are buried close to the nucleus and rarely get involved; it is the outermost electrons — the valence electrons — that reach out and interact with neighbouring atoms. Think of an atom as a person in a crowd: only their outstretched hands (the valence electrons) can shake, grab, or share with the people around them.
The valence electrons are those in the highest-occupied shell. Carbon (1s2 2s2 2p2) has 4 valence electrons; oxygen (2s2 2p4) has 6; sodium (3s1) has just 1. For the main-group elements this count equals the group number in the periodic table, which is why it is so easy to read off. That number sets how many bonds an atom tends to form: carbon's 4 valence electrons let it form 4 bonds and build the endless chains and rings of organic chemistry and polymers.
Valence electrons are the currency of bonding. Whether an atom gives them away (making a positive ion), grabs more (a negative ion), shares them (a covalent bond), or pools them communally (a metal) is decided here. Nearly every material property traces back, through bonding, to how many valence electrons the atoms carry and how tightly they are held.
Silicon sits below carbon and also has 4 valence electrons, so it too forms 4 directional bonds — which is why silicon builds a diamond-like crystal and underpins both ceramics (as silica) and the entire semiconductor industry.
Four valence electrons, four bonds: the signature of carbon and silicon.
The neat group-equals-valence rule works cleanly for the main-group (s and p block) elements. Transition metals are messier because their d electrons can also participate, giving them several possible valences (iron can be +2 or +3).