From GameBrew - a wiki dedicated to Video Game Homebrew.
Boots NTR CFW. NTR is a CFW that needs to be launched manually before activated. With NTR you have a wide range of options like cheatmenus, streaming (no capturecard required) and a lot more. It's very plugin friendly. This is just a crash course, I use it mostly for cheats since I hate grinding in some games.
BootNTR isn't depending on your CFW you are running. BootNTR need to have support for the firmware. I suggest you use BootNTR Selector since it have higher compability and faster updates than the original.
About Mode3 Build
BootNTR-Mode3 is a special build of BootNTR for running NTR with extended memory games on Old3DS. It is no use to install BootNTR-Mode3 on New3DS since the original one works just fine. See https://github.com/44670/BootNTR/wiki/Extended-memory-games-on-O3DS for how to launch extended memory games with NTR.