The number of electron-pair bonds between two nuclei in any given Lewis formula (electron dot or Lewis structure). For example, in ethene the bond number between the carbon atoms is two, and between the carbon and hydrogen atoms it is one.
Source:
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1090 (https://doi.org/10.1351/pac199466051077)