What "without re-encoding" means
An AAC sound track is a sequence of small compressed packets, each about 21 ms long at 48 kHz. Extracting without re-encoding means those packets are copied unchanged into a new M4A file; nothing is decoded and compressed again, so not a single bit of the sound differs from what is inside the video.
Converters that "convert MP4 to M4A" by re-encoding AAC at 128 or 256 kbps lose a little quality each time and change the file's bitrate. Here the bitrate, sample rate and channels are always the video's own.
Why it finishes in seconds
Copying packets needs no decoding, only reading. In tests, a 90-minute MP4 gave its 87 MB M4A in 6 to 14 seconds, and a 2.08 GB MOV gave its sound in under 3 seconds, including on Firefox. The picture data is skipped, not read into memory.
Phones work just as well, because memory use is about the size of the sound itself.
Proof that the audio is identical
The tool's tests compare a SHA-256 hash of every sound packet in the video with the same packets in the M4A; they match exactly for MP4, MOV, MKV and MPEG-TS sources (TS only drops the 7-byte ADTS frame headers that M4A doesn't use). For MP4, MOV and MKV sources the start delay of AAC (1,024 samples) is carried over in the M4A's edit list, so the file plays exactly as long as the video's sound: 10.000 seconds stays 480,000 samples at 48 kHz.
Your own check: the result shows the same bitrate as the source, and the badge "No re-encoding" appears only when the packet copy succeeded.
Where M4A plays, and ringtones
M4A (AAC in an MP4 audio file) plays on iPhone and iPad, Android, Windows 10 and 11, macOS, Chromebooks, VLC and most car systems from the last decade, and imports into Apple Music, iTunes and most editors.
For an iPhone ringtone, cut a section of up to 30 seconds with "Cut a section", rename the .m4a to .m4r and add it through Finder or iTunes on a computer.
Videos whose sound is not AAC
M4A can only hold AAC (or Apple Lossless) without re-encoding. A WebM or MKV with Opus sound gives the original as .ogg, Vorbis as .webm, FLAC as .flac, camera PCM as .wav and Dolby Digital as .mka, and the result explains why. If you need a file that plays everywhere, use MP4 to MP3 instead; that path re-encodes once.