The coordination number refers to the total number of ligands that surround a central metal ion in a coordination compound.

In these compounds, the central metal ion is encircled by ligands, which can be either molecules or ions that provide electron pairs to the metal ion. The coordination number specifically indicates how many ligands are directly attached to the metal ion. For instance, in a complex with a coordination number of $4$, there are four ligands that are directly bonded to the central metal ion.

Several factors influence the coordination number, including the size of the metal ion and the size of the ligands. Larger metal ions are capable of accommodating more ligands, which results in a higher coordination number. Conversely, smaller ligands can fit more snugly around the metal ion, which can also lead to an increased coordination number.

Additionally, the coordination number is affected by the charges of both the metal ion and the ligands. For example, a metal ion with a charge of $2+$ can typically bond with a greater number of negatively charged ligands compared to positively charged ones.

In summary, the coordination number is defined as the number of ligands that are directly bonded to a central metal ion within a coordination compound. This number is influenced by the sizes of both the metal ion and the ligands, as well as their respective charges.