Time for a fight! Legate Cipius will advise you that the Stormcloaks are at the city and will tell you to head to the frontline and meet with Legate Rikke. Leave Dragonsreach and follow the marker to the entrance of Whiterun. Out here, speak to Legate Rikke and then it's time to defend the barricades.
If you want, you could just jump outside the barricade and start spamming your best Destruction spells (in case you're a magic user), use as many arrows as you can or simply equip your best Heavy Armor and start attacking nonstop. In the end you must get that counter down to 0%. If you fail to stop them at the barricade, stop them at the drawbridge (but note even if the barricade falls, that area still acts as a great funnel and should be used as such).
Once you are done you will be told to return to General Tullius at Solitude and the next quest, 'Reunification of Skyrim', will start.
Note: That you can just run away and wait for the battle to end. The Legion will still win either way, but you won't get the prize in the next quest.