IIRC parsers let it reconstruct metadata from files that aren't muxed, or inaccurately muxed. For instance, you'd need one to read raw .h264 files properly into .mp4.
Parsers typically are used to correctly demarcate packet boundaries in (coded) bitstreams e.g. H.264 bitstream is partitioned into NAL units and the parser assembles all relevant units for a single frame/slice so that the decoder gets everything it needs to decode that sample, nothing more, nothing less.
Well I should hope it does more by now because that's not enough information to mux an H.264 stream. You need to recover PTS/DTS offsets, keyframe types, SPS, etc.