A travel day is always from 0:00 to 23:59 CET. During that time, you can board as many trains as you want.

What I want to know is, if I take a train the 15 June for instance, and it takes just 3  hours, the day next are deducted from the remaining 21 hours or it's counted as another travel day?

The pass does not count hours, only days. If you want to take a train with your pass, then you need a valid travel day. If you also want to take a train the next day, then you need another travel day.

One extra point - you only consider the scheduled departure time in deciding which travel day is used so, for example,  if you are on a train that continues after midnight on a Monday that train is taken from the Monday travel day. If you then board a further connecting train after midnight that train will use Tuesday as a travel day. The only exception I am aware of is on the very last day of validity of a pass when all travel has to be completed by midnight.

Another example would be a night train scheduled to leave at say 2330 CET on Monday, but delayed till after midnight - that would be added to your trip with the scheduled time and taken from Monday as a travel day.