This morning I 've click on some links from search results then when I browse back to the search result again, it displays the number of time and the time (not local time) of those clicks.

So they might have add in their algorithm for ranking.
You be be better ranking if there are more clicks and your ranking can depend of what time now.

For example if most traffics came in the morning you'll gain 1 or 2 ranks and at night you will loose these rankings gain. Other website that was 1 or 2 rank under your link will gain it according to number of clicks and time.

I'm not sure for what I wrote but can be something like this.

They might violate your privacy if they can check time and clicks from your browsing habits.