The Spanish verb dejar (to leave, let) comes from Latin laxare (to loosen, release). In Late Latin, this verb was combined with the prefix de, which commonly conveys separation or removal. The resulting form, delaxare, meant something like "to release, let go." When you let something go, you're leaving it behind or letting it go. From there, regular sound changes carried the word into Spanish. The unstressed vowel in delaxare dropped, yielding Old Spanish dexar, and the Old Spanish x later shifted to the modern j, giving dejar.

A closely related Spanish word is 'relajar' (to relax), which also comes from Latin 'laxare'. While 'dejar' took on the meaning of leaving or letting go, 'relajar' maintained the original sense of loosening or becoming less tense. Another related word is 'laxo' (loose, slack), which more directly preserves the meaning of the Latin root.

English speakers might recognize the connection to words like 'lax' and 'relax', which share the same Latin ancestor 'laxare'. Just as 'dejar' developed from the idea of loosening into leaving, these English words maintained meanings related to looseness or the release of tension. The word 'laxative' is another English relative, referring to something that loosens the bowels.