And as long as you can play a move every 10 seconds, you can never lose on time.
what does 15/ 10 mean?

what does 15 / 10 mean?
15 minutes to start with for each side. After each move is made, 10 seconds is added on to the clocks

Bitte alles auf Deutsch übersetzen
Hallo! Ich kann ein bisschen Deutsch sprechen. 15 Minuten zu Beginn für jede Seite. Nach jedem Zug werden den Uhren 10 Sekunden hinzugefügt

What is the point of this rule?
The point is to give you time to checkmate and think in the endgame I believe, in case time is running low. Then it does not become a test of mouse speed and accurate premoves but endgame skill.
I don't like it because it encourages negative and bad play. I don't play any increment above 5 seconds because people can still lose on time with 5 secs increments. There's not much point in playing fast chess with a clock and a 10 second increment.
You wouldn't say, my midgame was 2.1% but I still won.

In my first 15-10 game my opponent was down to 1:34 and then his time seemed to be increased by much more than 10 seconds per move. Was my perception faulty or is there more to this rule?

I wonder if neuroscientists have explored the perception of time using increment chess. Are records kept of the timing of each move and each added time?

IOW, can I go back over that drawn 15-10 time and revisit the time flow? Has this aspect of the topic been explored here or elsewhere? What hath Bobby Fisher wrought?

An example night help. We start a 15/10 game and its my move first. The clock starts and I make a move after 3 seconds, so I've got 14m57s left, but i get an extra 10s per move so the clock now shows 15m07s. My second move takes 27s so 15m07s - 27s = 14m40s left but again I get 10s for the 2nd move=14m50s.
Does that help?

Bobby Fischer, the former world chess champion, invented the revolutionary game of Chess960 and patented the innovative timing method now known as Increment or Bonus.
"A specified amount of time is added to the player's main time each move unless the player's main time ran out before they completed their move."
What is the point of this rule?
The point is to give you time to checkmate and think in the endgame I believe, in case time is running low. Then it does not become a test of mouse speed and accurate premoves but endgame skill.