Depends on what you are refering to.
Session object or just the term?
Cookies are small files that contain data specific to a website. It is used as state mechanisim for HTTP (a stateless protocol) to store things like login info, session id or cart id, etc. This can be stored in the server or client.
Sessions are either objects associated with a specific socket connection, a logical connection (one where the socket may disconnect, but will re-connect within a short time frame), or may be of something else, but still generally pertaining to a state mechanisim.
If we're talking web application context:
Each web browser transaction is a separate connection, so the web server often needs to be able to keep track of which comes from which browser, to tie the individual transactions into a conversation. The most popular underlying mechanism is cookies. The server sends the browser a cookie as part of the first transaction response and, thereafter, every time the browser sends a transaction it includes the cookie. Cookies typically contain random strings of characters which uniquely label the browser.
A Session object is used in Serlvets and JSPs as a higher level abstraction of the same thing. The session object retains data about the conversation between transactions. The web server normally implements this by automatically creating a random cookie associated with the Session object and, whenever a transaction is received, it looks for the cookie and finds the relavant session object.