A9LH (or arm9loaderhax) is a system exploit that takes control over your system very early on boot, making it possible to run (on boot) custom software not signed by Nintendo, such as a Custom Firmware and that otherwise would be rejected by the console.
Luma3DS is your Custom Firmware (what gets loaded by A9LH on boot), and this is what makes it possible to install unsigned apps and games to your homemenu, among other things. One could run Luma3DS (or another CFW) without setting up A9LH. A9LH just makes it more enjoyable since it boots faster and is a more permanent hack than others.