Merge conflicts appear when changes in multiple branches cannot be combined automatically by Git. This often happens in shared repositories where contributors edit the same lines of code or files. GitHub provides an online editor for simple conflicts, available through the pull request’s 'Resolve conflicts' button. For more complex conflicts, use the command line: `git fetch`, `git checkout branch_name`, `git merge base_branch`, and then manually edit the conflicting files. After resolving conflicts, commit the changes and push back to the pull request branch. Careful conflict resolution ensures a smooth merge process and reduces future conflict likelihood.