“Another” is normally used to mean “one more”. For example, you can ask your mother for another bowl of ice cream, or another plate of puris. The word can be used with both singular and plural nouns; when used with the latter, it is followed by “few”. The Registrar will be retiring in another few days. The use of the word “another” also suggests that you have more than two choices available. If you are in a showroom and you ask a salesperson to show you “another car”, you are telling the individual that you want to see some other car — you are not interested in the ones that have been shown to you so far.
“Other”, on the other hand, suggests that you have only two choices available. For example, if you were to say, “I am not interested in this car, but am interested in the other”, what you mean is that you like the second car. A car that you have already seen. The choice here is between two cars.