Visual Studio 2013 does not offer to do merge on Git pull
In my case I could not see the Resolve the conflicts option because I had local changes not committed yet and I was trying to sync with the remote changes. As soon as I committed my local changes and then tried a sync again, Resolve the conflicts link appeared.
So the point here is: commit your changes first and then try to sync. A merge will start and Visual Studio will allow you to go through each of the conflicts.
I have encountered the same issue where "An error occurred. Detailed message: 1 conflict prevents checkout" is shown where there's no option to resolve the conflict as shown in Leinel's answer.
The reason was due to an untracked file that is the same file that is to be pulled. I just deleted the untracked file and retried the pull.
I had the same issue. It turns out that I had an untracked file that needed to be included. Therefore, check in Changes tab for untracked files.