This article takes you beyond the common but important observations about the differences between "salir" and "dejar" as stand-alone verbs. It concludes the story about the verb "dejar" by examining its meanings as a helping verb.
"Dejar" in All Its Glory as a Helping Verb
The verb dejar, used alone, means to leave something or someone behind. Hence it can translate as to abandon, to jilt, to leave standing at the altar, etc., using a direct object (noun or pronoun). Dejar also can mean to bequeath, when used with an indirect object pronoun. But beyond its fundamental meaning and how dejar differs from salir, it has other uses which increase its importance and frequency in the language.
There are two ways in which dejar is used as an auxiliary verb. In one case, it is directly followed by an infinitive. When this occurs, it means to allow or to let + verb: Su padre no la deja salir con ese muchacho. (Her father won't let/allow her to go out with that guy.) This usage is quite straight forward.
When used with the preposition de before the infinitive (dejar + de + infinitive), it means to quit or to stop doing something (or to not stop): Mis primos no dejan de hablar. (My cousins won't stop talking). Sometimes, the verb parar (literally to stop, as in a car) is substituted in this same structure. Do you see that in English, the verb following the verb to stop is in the gerund form? This is worth a passing comment: There is one universal rule when contrasting English with Spanish grammar which is 100% reliable. Whenever a verb follows a preposition in English, the verb appears in the -ing form, whereas in Spanish, it always will remain in the infinitive.
This last structure is common in imperatives, or commands: Deja de fumar. (Stop smoking.)
Used with en, instead of de, dejar means to leave in such-or-another condition, as in Déjame en paz. (Leave me in peace/alone.) Another example: La guerra dejó la ciudad en ruinas. (The war left the city in ruins.) Note that the preposition en does not always have to immediately follow the verb.