What is the role of aspect in Russian?

The two forms of aspect in Russian (the imperfective and the perfective) essentially function in the same way as the perfect and imperfect tenses do in other languages.

For example, if in English you wish to describe an unfinished action or a repeated action (e.g. "I was reading the book" or "I read the book every day", then this would correspond to the imperfective aspect in Russian: "Я читал книгу".

However, if you wish to express that you completed the action of reading the book, then the perfective aspect is used: "I finished reading the book" "Я прочитал книгу". 

The perfective aspect is used primarily for one-off actions that are completed, whereas the imperfective typically denotes an unfinished process or a habitual action.