Where does the latin word diligent come from?

The Latin word "diligent" comes from the Latin word "diligens", which is the present participle of the verb "diligere".

* "diligere" means "to love, to esteem, to value"

The word "diligens" therefore literally means "loving, valuing, esteeming," and in its metaphorical sense, "giving careful attention to, assiduous, hardworking."

This reflects the core meaning of "diligent": someone who is dedicated and puts effort into something they value.