Thanks for your question.
A day on a Eurail pass is usually one 24 hour period. Travel starting within that 24 hour period uses up 1 day on a Eurail pass. 3 days on a Eurail pass means three 24 hour travel periods starting at 12am, not three train trips. If you choose a pass with 3 flexible travel days over two months, you can use those 3 days at any time within those two months. If you like, you can travel to as many places as possible in one 24 hour period. A 24 hour period on a Eurail pass generally starts at 12am and ends at 11:59pm the same day.
So you could use it for like June 10, 16 & 20. Or you could use it June 20-22. June 23 would be considered a 4th day.
Hope this helps,
The straight (continuous) days option are only available on the Select or Global Eurail passes which you would buy if you are planning to travel within 3 countries or more. The continuous option is cheaper on these passes and it is a good option if you plan to travel almost every day. The regional and 1 country passes only have the flexi days option but you can pick consecutive days if you wish. For more info, see http://www.eurail.com/eurail-find-the-best-pass