Another is an adjective and a singular pronoun. It means “one more.”

I have already finished one ice cream, but I want to keep eating. I would like another ice cream, please.

I don’t have enough cars. I need to buy another.

Other is an adjective. It means “something different.”

I don’t like these songs. I want to sing some other songs.

Others is a plural pronoun. It means “more things.”

I don’t like these songs. I want to sing some others.

The other is a singular pronoun. It means “one out of two things.”

I have two shoes. One is for my left foot. The other is for my right foot.