Here, "one" is referring to the "day". So it means, live/enjoy/feel "this day" (today) fully. Enjoy the moment. Live in the now. That's basically what it's saying

I like this paragraph. It reminds me not to be trapped by the bitterness of yesterday or to be anxious by the seemingly dreadful tomorrow. I should live this life I have today, to the fullest. I guess that's what the author was trying to say.

The word "this’’ is making us realize that this time we are living right now is very important. Very beautiful lesson to always keep in mind.

The meaning of the sentence is straightforward. The only odd thing about the sentence is the use of the determiner "this". It is odd because there is only one today, so why would one need to specify it with a determiner. All of these sound odd but are not wrong: "our todays" "these todays" "some today" "any today" "no today", etc. All of these are odd, but not wrong. They sound poetic.