The Battle of the Yellow Fork is a minor engagement in the War of the Five Kings. It occurs off screen between "The Old Gods and the New" and "A Man Without Honor." The army of House Stark in the Westerlands moves west from Oxcross to attack a force of House Lannister conscripts at the Yellow Fork.
Having won a trio of victories in the Riverlands and a decisive victory at the Battle of Oxcross the army of House Stark under the command of King Robb I pushes further into the Westerlands. The victory at Oxcross has left the region lightly defended.
Lord Rickard Karstark reports taking so many Lannister prisoners that the Stark cells are overflowing. Talisa Maegyr continues to treat Robb's wounded along with those of his enemies following the battle.
The volume of prisoners leads to Jaime Lannister being housed with another man for the first time since his capture. This affords him the opportunity to make an escape attempt, murdering his cellmate Alton Lannister and killing Torrhen Karstark. He is recaptured shortly afterwards.
In the books
In the A Song of Ice and Fire novels there is no battle of this name. The location Yellow Fork is not mentioned in the books. However, the battle following the Battle of Oxcross is the Battle of Ashemark. The Season 2 bluray confirms the two battles are the same as the War of the Five Kings feature mentions Robb sacks Ashemark after his victory at Oxcross.