A travel day lasts 24 hours from midnight to midnight. On each travel day you have access to the train networks and participating ferry companies where your Eurail pass is valid.
A pass with "10 or 15 days within 2 months" means that you get 10 or 15 travel days of train travel within a period of 2 months. This type of pass is sometimes referred to as a "flexi pass".
A pass with "1 month continuous" means that each day during a period of 1 month is a potential travel day during which you can travel by train. This type of pass is sometimes referred to as a "continuous pass".