"You can lead a horse to water, but you can't make it drink" is an English proverb.
If you want the horse to drink, the most you can do is lead it to water; after that, the horse drinks only if it wants to.
More generally, the proverb is used in the senses of "there's only so much you can do" or "people will do what they want" or "you can't help people who don't want to be helped".
This proverb is one of the oldest in English , having been recorded in Old English Homilies , 1175:
Hwa is
thet mei thet hors wettrien the him self nule
drinken [who can give water to the horse that will not drink of its own accord?]
So "Chuck Norris can lead a horse to water AND make it drink" simply reverses the proverb: Chuck Norris can do something which the proverb says is impossible.
(The humour is partly from the appropriation of a commonplace proverb for Chuck Norris purposes.)
Something similar would be "Chuck Norris can eat his cake and have it too", reversing the proverb
"You can't eat your cake and have it too".
(Once you eat your cake, you'll no longer have it with you: this proverb is these days more commonly stated as "you can't have your cake and eat it too".)
english.stackexchange.com/users/77/ShreevatsaR
There is an idiom in English : You can lead a horse to water, but you can't make it drink.
Even favorable circumstances won't force one to do something one doesn't want to, as in We've gotten all the college catalogs
but he still hasn't applied
--you can lead a horse to water.
This metaphoric term dates from the 12th century and was in John Heywood's proverb collection of 1546.
It is so well known that it is often shortened, as in the example.
The whole notion here is that Chuck Norris has superpowers, making possible the impossible even.
These jokes are only funny when you hear many of them in a row and one seems to outdo the other.
english.stackexchange.com/users/None/
The dynamics of the joke have been explained so I won't rehash that
but I don't see the meta-joke being mentioned here
so I'll explain it.
A kind of meta-joke, a joke above the jokes, is to tell a series of really unfunny jokes.
So while the jokes in and of themselves aren't funny the string of jokes clearly not meant to be funny can be funny.
If it's just one joke you might say, "Meh, that wasn't funny."
But a barrage of really stupid jokes, if they are ridiculously unfunny like the one above, is funny.
And finally it's kind of an inside joke that some people actually find the unfunny jokes funny.
That's a meta-joke on top of the meta-joke.
P.S.
I don't find Chuck Norris jokes funny either, but I get it.
english.stackexchange.com/users/1702/Kludge
This is related to the idiom: You can lead a horse to water, but you can't make it drink.
Meaning: People, like horses, will only do what they have a mind to do. or Something that you say which means you can give someone the opportunity to do something, but you cannot force them to do it if they do not want to.
So the sentence you refer to is a joke which points out the determination (decisiveness) of Chuck Norris.
english.stackexchange.com/users/127/Mehper C. Palavuzlar
Well I guess Chuck Norris is so physically capable that he can "force" a horse to drink water no matter what, even if it doesn't want to, so you'd better watch out if you mess with Chuck Norris.
english.stackexchange.com/users/1698/trusktr
Chuck Norris can lead a horse to water  and  make it drink.   I read this on  http://chucknorrisfacts.com .  What I think this sentence means, is: Chuck Norris can take his horse to where the water is and then his horse will drink the water. So, what is funny about this? Isn't it something pretty normal?
What does this mean: 'Chuck Norris can lead a horse to water AND make it drink'? Why is it funny?
english.stackexchange.com
<meaning><humor>
english.stackexchange.com/questions/4009
english.stackexchange.com/users/530/Rakesh Juyal
This joke plays on the notion that Chuck Norris is so powerful that he is able to do something which the English proverb says is impossible. The notion is that Chuck Norris has superpowers. It is an English proverb dating back to the 12th century meaning you can bring the horse to the water, but you cannot make it drink.  There is only so much you can do to help people, you cannot force people to do something they don't want to do. By extension, it is suggesting Chuck Norris has exceptional powers because he actually can make the horse drink. Some people do not find this a funny joke, but understand what is meant. 
This joke plays on the notion that Chuck Norris is so powerful that he is able to do something which the English proverb says is impossible. The notion is that Chuck Norris has superpowers. "You can lead a horse to water, but you can't make it drink"  is an English proverb.  If you want the horse to drink, the most you can do is lead it to water; after that, the horse drinks only if it wants to. Meaning:  People, like horses, will  only do what they have a mind to do. The whole notion here is that Chuck Norris has superpowers or the determination to make possible the impossible.
Chuck Norris can lead a horse to water AND make it drink simply reverses the proverb: Chuck Norris can do something which the proverb says is impossible. This joke plays on the notion that Chuck Norris is so powerful that he is able to do something which the English proverb says is impossible.
"You can lead a horse to water, but you can't make it drink"  is an English proverb.  If you want the horse to drink, the most you can do is lead it to water; after that, the horse drinks only if it wants to. Meaning:  People, like horses, will  only do what they have a mind to do. The whole notion here is that Chuck Norris has superpowers or the determination to make possible the impossible.
This joke plays on the notion that Chuck Norris is so powerful that he is able to do something which the English proverb says is impossible.