This is basically the same as asking what would happen if wizards had cell-phones, or wireless telegraphs. You can look at real-world reactions to those, and extrapolate back in time.
Twelfth's answer covers the diplomatic and militaristic angles, which was one of my first thoughts as well. This would allow kingdoms to more easily span larger areas. It could also be used by spies, for espionage. Which raises an interesting question: If two wizards are communicating, how secure is that communication? Could another wizard "hack into" the channel, and eavesdrop on them?
But here's some additional uses:
News. Humans seems to be fascinated with distant events, and a network of wizards could set up a sort of news-wire for distributing notable world events -- weather patterns, wars, crimes, politics, religious matters, sporting events, etc... Of course, a more nefarious media might also put a "spin" on the news, to tell the narrative they want. News can also be used to facilitate:
Trade. If you were a merchant, and you got word that there was a famine in a town three days to the north, you might consider making a trip up that way with a food surplus, secure in the knowledge that you'd have a good market. You might not have been planning to make that trip before, so you'd be willing to pay someone to update you on recent changes to nearby market conditions. As user3913060 points out, they may well choose to keep economic information to themselves, and profit from it more directly (rather than sell it to merchants). This may depend on the ethics of each individual wizard. Or there may be laws in place to prevent this kind of "inside trading" (but how could such a law be enforced?). At any rate, if there's no easy way to transport goods, the wizards may well develop a currency based on promissory notes rather than physical possession. Then they could broker trades of the ownership of one commodity on one side of the globe with that of another commodity on the other side of the world, without the goods physically exchanging hands, much like commodities traders today.
Correspondence. Wizards could set up a sort of telegram post-service allowing individuals to send letters to loved ones (or business associates) who are located far away. This might encourage more long-distance traveling, and perhaps exploratory expeditions (if they can be funded). Imagine if Christopher Columbus could have instantly provided daily reports on his discovery of the New World back home.
Cultural Diffusion. "It's a small world" as the saying goes. If you can receive messages from people anywhere in the world, even if its not done frequently, or on a personal basis, you're likely to have at least heard stories of the way other people around the world act. This wouldn't be hearsay from some single adventurer's tale, but would be (relatively) factual information. Eventually, you'd probably become more accustomed to other cultural beliefs and behaviors, to where they didn't seem so strange. This could also be used to share what we would call "IP" today (intellectual property) -- music, art, literature, even theories and inventions, could all be shared much faster.
The limiting factor here is how common these wizards are, and how available they make their services (and for what price, and with what level of accuracy?).
And finally, these wizards would obviously share silly pictures of their cat familiars with each other.