So after 25, we'll go back to counting by one, is the one minute. We have 25, 26, 27. The minute hand has gone past 27 of these marks, meaning that it is 27 minutes past the hour. Let's try another one. The hour hand is between the four and the five, which means it's after 4 o'clock. It's some amount of minutes after four, but it is not yet five.
Perhaps you have heard "I'll be back in 15" as a short form of "I'll be back in 15 minutes". That means "I will be gone for 15 minutes and then I will return. It is nothing to do with the actual time on the clock. If I leave at 9:30 and say. "I'll be back in 15" and I return at 9:45 I will have been gone for 15 (minutes).
These expressions, of course, include such simple and frequent conversations as those relating to time! Now, to your question, "What is "It's ten after eleven" mean?It mean 11:10?" I will retype you example, including (in capitals) the omitted (understood) parts of your example: "It's ten MINUTES after (or PAST) eleven O'CLOCK (or AM or PM)."
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15 minutes past 8 means