Explain different types of sessions in Magento (e.g. customer/session, checkout/session, core/session) and the reason why you store data in different session types?

Customer sessions stores data related to customer, checkout session stores data related to quote and order. They are actuall under one session in an array. So firstname in customer/session will be $_SESSION['customer']['firstname'] and cart items count in checkout/session will be $_SESSION['checkout']['items_count']. The reason Magento uses session types separately is because once the order gets placed, the checkout session data information should get flushed which can be easily done by just unsetting $_SESSION['checkout'] session variable. So that the session is not cleared, just session data containing checkout information is cleared and rest all the session types are still intact.