Why is the nacl extracted with water three times?

Because each time you extract, you only get ~50% of what was in there. So, after 1 time, you have 50%. The 2nd time, you get 50% of the 50% left from trial 1 (so, 25%) - giving you a total of 75% of the NaCl after 2 extractions. Trial 3 gets 50% of the remaining 25% (which is 12.5%), so after 3 trials, you have extracted ~87.5% of your NaCl. Doing it 4 times only gets you another 6.25%, 5x is an extra ~3% - so on and so forth.

You do it 3 times to get the maximum extraction for only a few trials. Anything more than 3 or 4 times is not worth the effort for the small yield!