Learn Spanish (Latin America): Le entregué el efectivo al cajero.

If you wrote entregé, the "g" would sound like an English "h" (because "g" before "e" or "i" makes a soft sound in Spanish). To keep the hard "g" sound from the infinitive entregar, you have to add a silent "u". This happens with all verbs ending in -gar when you use the yo (I) form in the preterite (past) tense: -gar changes to -gué.

Why do we need the pronoun Le at the beginning if we already say al cajero (to the cashier) at the end?

In Spanish, it is usually required to use an indirect object pronoun (like le, meaning "to him" or "to her") even when you explicitly name the person later in the sentence. It feels redundant in English (like saying "To him I handed the cash to the cashier"), but in Spanish, le acts as a necessary tag that points ahead to al cajero.

What is al short for in this sentence?

al is a mandatory contraction of the preposition a (to) and the article el (the). Whenever a is followed directly by el, they combine into al. So, al cajero means "to the cashier".

I've seen efectivo used to mean "effective". Does it also mean "cash"?