You must journey back to see the Greybeards on High Hrothgar to inquire about the Dragonrend shout that the old Blade, Esbern, says might be the only way to defeat Alduin the dragon, as the ancient Nords used it to do so thousands of years ago when he last threatened Skyrim.
You arrive at the mountain temple and speak to Arngeir about Dragonrend and other things. At first he is reluctant to have anything to do with your efforts to learn Dragonrend, especially after learning that you’re now working with the Blades, but when a thunderous roar in the language of the dragons, like the one that first summoned you to High Hrothgar after you killed the dragon near Whiterun, eminates from somewhere outside the temple, Arngeir relents and says that Paarthurnax, the leader of the Greybeards, has requested to meet with you at his dwelling place at the very top of the mountain.
He takes you outside to some steps leading up to a stone archway, beyond which lies the path to the top of the mountain. But the path to the top is hazardous with frozen ice storms, so in order to make your way up there, he first teaches you a Clear Skies shout. Use this new shout to dispel the ice storm effect from underneath the archway and proceed up the mountain, continuing to use the shout to dispel the hazardous frozen storm effects you encounter as you go.
You arrive at the Throat of the World to find that Paarthurnax, leader of the Greybeard order, is a dragon. He’ll explain that it is a custom among dragons to show each other their Thu’um before initiating a conversation, and that the elder should speak first. He’ll then release a gout of flame onto a wall, and by inspecting the words it left behind you can learn the shout he just used. Now use this new shout on Paarthurnax. On feeling your Thu’um he will agree with the opinions voiced by the Greybeards that your voice is quite strong and offer to answer any questions you have.
Unfortunately, Paarthurnax doesn’t know Dragonrend either. In fact, he thinks the only way to learn the Shout would be to venture into the timewound that exists here on the mountain, travelling back in time thousands of years to meet the first humans that Paarthurnax taught to use dragon shouts, who eventually created Dragonrend and used it to defeat Alduin.
The conversation then turns to how you might exploit the timewound and take yourself back in time. We now learn some interesting lore about the Elder Scrolls themselves, but the basic idea is that if you can acquire an Elder Scroll and bring it back to Paarthurnax, he can cast you back in time to Alduin’s first defeat.
Unfortunately Paarthurnax has no idea where to find an Elder Scroll. He suggests you talk to Arngeir the Greybeard or Esbern the Blade for advice.