Not really related to this answer, but I'd ditch git pull, which just runs git fetch followed by git merge. You are doing three merges, which is going to make your Git run three fetch operations, when one fetch is all you will need. Hence:

git fetch origin   # update all our origin/* remote-tracking branches

git checkout demo         # if needed -- your example assumes you're on it
git merge origin/demo     # if needed -- see below

git checkout master
git merge origin/master

git merge -X theirs demo   # but see below

git push origin master     # again, see below

Controlling the trickiest merge

The most interesting part here is git merge -X theirs. As root545 noted, the -X options are passed on to the merge strategy, and both the default recursive strategy and the alternative resolve strategy take -X ours or -X theirs (one or the other, but not both). To understand what they do, though, you need to know how Git finds, and treats, merge conflicts.

A merge conflict can occur within some file1 when the base version differs from both the current (also called local, HEAD, or --ours) version and the other (also called remote or --theirs) version of that same file. That is, the merge has identified three revisions (three commits): base, ours, and theirs. The "base" version is from the merge base between our commit and their commit, as found in the commit graph (for much more on this, see other StackOverflow postings). Git has then found two sets of changes: "what we did" and "what they did". These changes are (in general) found on a line-by-line, purely textual basis. Git has no real understanding of file contents; it is merely comparing each line of text.

These changes are what you see in git diff output, and as always, they have context as well. It's possible that things we changed are on different lines from things they changed, so that the changes seem like they would not collide, but the context has also changed (e.g., due to our change being close to the top or bottom of the file, so that the file runs out in our version, but in theirs, they have also added more text at the top or bottom).

If the changes happen on different lines—for instance, we change color to colour on line 17 and they change fred to barney on line 71—then there is no conflict: Git simply takes both changes. If the changes happen on the same lines, but are identical changes, Git takes one copy of the change. Only if the changes are on the same lines, but are different changes, or that special case of interfering context, do you get a modify/modify conflict.

The -X ours and -X theirs options tell Git how to resolve this conflict, by picking just one of the two changes: ours, or theirs. Since you said you are merging demo (theirs) into master (ours) and want the changes from demo, you would want -X theirs.

Blindly applying -X, however, is dangerous. Just because our changes did not conflict on a line-by-line basis does not mean our changes do not actually conflict! One classic example occurs in languages with variable declarations. The base version might declare an unused variable:

int i;

In our version, we delete the unused variable to make a compiler warning go away—and in their version, they add a loop some lines later, using i as the loop counter. If we combine the two changes, the resulting code no longer compiles. The -X option is no help here since the changes are on different lines.

If you have an automated test suite, the most important thing to do is to run the tests after merging. You can do this after committing, and fix things up later if needed; or you can do it before committing, by adding --no-commit to the git merge command. We'll leave the details for all of this to other postings.

1You can also get conflicts with respect to "file-wide" operations, e.g., perhaps we fix the spelling of a word in a file (so that we have a change), and they delete the entire file (so that they have a delete). Git will not resolve these conflicts on its own, regardless of -X arguments.

Doing fewer merges and/or smarter merges and/or using rebase

There are three merges in both of our command sequences. The first is to bring origin/demo into the local demo (yours uses git pull which, if your Git is very old, will fail to update origin/demo but will produce the same end result). The second is to bring origin/master into master.

It's not clear to me who is updating demo and/or master. If you write your own code on your own demo branch, and others are writing code and pushing it to the demo branch on origin, then this first-step merge can have conflicts, or produce a real merge. More often than not, it's better to use rebase, rather than merge, to combine work (admittedly, this is a matter of taste and opinion). If so, you might want to use git rebase instead. On the other hand, if you never do any of your own commits on demo, you don't even need a demo branch. Alternatively, if you want to automate a lot of this, but be able to check carefully when there are commits that both you and others, made, you might want to use git merge --ff-only origin/demo: this will fast-forward your demo to match the updated origin/demo if possible, and simply outright fail if not (at which point you can inspect the two sets of changes, and choose a real merge or a rebase as appropriate).

This same logic applies to master, although you are doing the merge on master, so you definitely do need a master. It is, however, even likelier that you would want the merge to fail if it cannot be done as a fast-forward non-merge, so this probably also should be git merge --ff-only origin/master.

Let's say that you never do your own commits on demo. In this case we can ditch the name demo entirely:

git fetch origin   # update origin/*

git checkout master
git merge --ff-only origin/master || die "cannot fast-forward our master"

git merge -X theirs origin/demo || die "complex merge conflict"

git push origin master

If you are doing your own demo branch commits, this is not helpful; you might as well keep the existing merge (but maybe add --ff-only depending on what behavior you want), or switch it to doing a rebase. Note that all three methods may fail: merge may fail with a conflict, merge with --ff-only may not be able to fast-forward, and rebase may fail with a conflict (rebase works by, in essence, cherry-picking commits, which uses the merge machinery and hence can get a merge conflict).