Correct spelling, explanation: allow comes from Latin allaudare, so, as you can see, the Latin root word has the double l. In general, while the words often change over the centuries, the consonants usually stay in their place as a spine of the word, which is why despite other changes, the double l stayed in allow.

Definition of allow:
verb
1. to give permission or to let somebody or something perform an action
As a boss, I can allow my workers to leave early on Fridays.
2. to give permission or opportunity for something to take place
The sunny weather allowed us to go on a camping trip.

Idioms with allow:
Allow (someone) free rein – to give someone complete freedom
My husband and I went out for the weekend to allow our children free rein in the house and let them have a party.

Incorrect spelling, explanation: there is no rule as to when l is doubled in root words. The main reason why allow is correct and alow is not, is the word’s origin, which is the Latin word allaudare with a double l. Another reason may be connected to the understandability – while allow is clearly a base word, alow might be mistaken for adjectives such as alight or aloud.