Why do we need to install gulp globally and locally?

You can link the globally installed gulp locally with

npm link gulp

TLDR; Here's why:

The reason this works is because gulp tries to run your gulpfile.js using your locally installed version of gulp, see here. Hence the reason for a global and local install of gulp.

Essentially, when you install gulp locally the script isn't in your PATH and so you can't just type gulp and expect the shell to find the command. By installing it globally the gulp script gets into your PATH because the global node/bin/ directory is most likely on your path.

To respect your local dependencies though, gulp will use your locally installed version of itself to run the gulpfile.js.

When installing a tool globally it's to be used by a user as a command line utility anywhere, including outside of node projects. Global installs for a node project are bad because they make deployment more difficult.

npm 5.2+

The npx utility bundled with npm 5.2 solves this problem. With it you can invoke locally installed utilities like globally installed utilities (but you must begin the command with npx). For example, if you want to invoke a locally installed eslint, you can do:

npx eslint .

npm < 5.2

When used in a script field of your package.json, npm searches node_modules for the tool as well as globally installed modules, so the local install is sufficient.

So, if you are happy with (in your package.json):

"devDependencies": {
    "gulp": "3.5.2"
}
"scripts": {
    "test": "gulp test"
}

etc. and running with npm run test then you shouldn't need the global install at all.

Both methods are useful for getting people set up with your project since sudo isn't needed. It also means that gulp will be updated when the version is bumped in the package.json, so everyone will be using the same version of gulp when developing with your project.

Addendum:

It appears that gulp has some unusual behaviour when used globally. When used as a global install, gulp looks for a locally installed gulp to pass control to. Therefore a gulp global install requires a gulp local install to work. The answer above still stands though. Local installs are always preferable to global installs.