Incorrect spelling, explanation: this spelling is wrong because there are no two l in the French original word (aligner). In English, we also don’t double the l and the correct spelling is align.

Correct spelling, explanation: origins of the word align are in French aligner, meaning line/in line. The original word is spelled with one l and thus the English word is also spelled with one l. Allign is incorrect.

Definition of align:
1. verb, to place something in the line or order; make equal or appropriate
At first, they had some problems with aligning the project to the site, but it turned out perfectly.
2. verb, to integrate with others who have the same point of view, aim
I align with this political party because I agree with most of their postulates.