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.