"И" means exactly "and", emphasises two (or more) pieces of information together.
Example: Я поеду в Москву и в Санкт-Петербург.
"А" has no exact translation into English, it is mostly translated as ""but" (sometimes as "and") and is used for 2 situations:
- With particle "НЕ": for more accurate description of the situation or action. Example: Я поеду в Москву, А НЕ в Санкт-Петербург. (or Я поеду НЕ в Москву, А в Санкт-Петербург.)
- With different subjects: for more accurate emphasis of the subject. Example: Я поеду в Москву, А ТЫ поедешь в Санкт-Петербург.
"A" should also be differentiated from "НО", which means exactly "but" and expresses opposition. Example: Я поеду в Москву, но не в Санкт-Петербург. - Unlike "A", it demonstrates a pricipial opposition to the first part of the sentence.
One more example: Я поеду в Москву, но ты поедешь в Санкт-Петербург. - (I'll go to Moscow, but you (must) go to St. Petersburg.)