Session is a group of tabs, which is relevant to a specific problem, for example: how to use ElasticSearch with MongoDB, or background information about TV show "The Wire".
Firefox
Save: right click on the tab bar and select "Bookmark All Tabs" (Shift + Ctrl + D);
Restore: click "Show your bookmarks" button on toolbar, navigate to the folder and click "Open all Tabs" at the bottom.
Chrome
Install extension "Session Buddy". It will help you to save and restore all open tabs as a "Session".
To sync sessions between browsers of different hosts, use "Settings -> Export" to save the session into a json file, copy this file to the target host, use "Settings -> Import" to import the session.