Why Does Halo 3 Let Me Record Game Clips?

You're likely thinking of Game DVR / Theater Mode, which was introduced in Halo 3: ODST (2009) and expanded in Halo: Reach (2010)—not in the original Halo 3 (2007).

Timeline

• Halo 3 (2007): No built-in recording or theater.
• Halo 3: ODST (2009): First Halo with clip capture (~30 seconds, saved to file share).
• Halo: Reach (2010): Full Theater Mode—longer clips, free camera, rendering, sharing.

If you're playing the original Halo 3 (via MCC or backward compatibility), you have no native recording. You might be recalling a later title, using a capture card, or the Xbox system-level Game DVR (double-tap Xbox button).