The fundamental definition of a conflict is that you touched some source line(s) that they also touched. For instance, given:
original line (in base): He said, "Hello world!"
your replacement: He said, "Hello wonderful world!"
their replacement: He said, "Goodbye cruel world!"
which line should Git keep, and which one should it discard, or should there be a third outcome entirely? Git does not know, so it leaves the task to you.
In this case, your ("HEAD") change was to remove every line by removing the entire file. Their change was to modify some line(s) of the file. Git doesn't know what to do: should it delete the entire file like you did? Should it keep their modified version? Or, perhaps there is some third way to deal with the problem.
It's generally easier to delete everything again than it is to reconstruct their version (although it's not really that hard either way), so Git leaves their version in the work-tree. If that's the correct answer, you can simply git add the file to tell Git: use that version. If deleting the file entirely is the correct answer, git rm the file to tell Git: delete the file entirely. If there's some third correct answer, edit the file as necessary to put in the correct contents, and git add the file to tell Git: use that version.
In any case, you have now resolved this particular file's conflict (once you have git add-ed or git rm-ed the appropriate final result). Resolve other conflicts if necessary, then finish the merge:
git commit
or (since Git version 2.12):
git merge --continue