Correct spelling, explanation: allow is a word of Latin origin (allaudare), which dictates the way it’s written, as well as its pronunciation. The spelling has significantly changed to fit English standards: au became ow, to make the pronunciation more intuitive, but the double l in allow stayed unchanged.

Definition of allow:
verb
1. to let somebody do something;
I allow my kids to eat sweets, but my husband wants them to only eat healthily.
2. to let something happen.
I left the window open to allow the warm wind to enter my apartment.

Idioms with allow:
Allow for something – to take a possibility into consideration and accommodate it
The hotel room is meant for two people, but it allows for an extra bed if needed.
Allow nature to take its course – to let a situation develop without interruption
I briefly prepared for my presentation, but when I went on stage to present it, I just allowed nature to take its course and in the end, the presentation went really well.

Incorrect spelling, explanation: because of the Latin origin – allaudare – the word has a double l, despite it not being necessary for pronunciation purposes. Visually, though, alow doesn’t look natural, as ll is quite often doubled in similar words.