When there is a conflict during a merge, you have to finish the merge commit manually. It sounds like you’ve done the first two steps, to edit the files that conflicted and then run git add on them to mark them as resolved. Finally, you need to actually commit the merge with git commit. At that point you will be able to switch branches again.
Quick Tip: You can use git commit -am "your commit message" to perform add and commit operations on tracked files simultaneously. (Credit: @vaheeds)