This hose is part of the secondary air pump system on 1999 to 3/2003 (march 2003 build date) E46 323i/325i/328i/330i models. This includes all 1999, 2000, 2001, and 2002 model year E46 3 Series, as well as the 2003 model years built before 03/2003 production.
The secondary air pump adds fresh air to the exhaust to help with cold start emissions and to heat the catalytic converters and O2 sensors. A broken hose likely won't cause any reliability or drivability issues but may cause a check engine light or lead to premature failure of cats or O2 sensors.
This is an air pump hose manufactured by Rein Automotive - an original supplier to BMW for many other hoses and lines. As an OEM it meets all of BMW's original design, fitment, and performance requirements and is TUV approved. OEM-type parts like Rein are the best alternative to more expensive Original BMW parts because they are virtually identical without the inflated price tag. This part has a two year warranty.
BMW Fitments:
3 Series
E46 (99-05) > 323Ci
E46 (99-05) > 323i
E46 (99-05) > 325Ci
E46 (99-05) > 325i
E46 (99-05) > 325xi
E46 (99-05) > 328Ci
E46 (99-05) > 328i
E46 (99-05) > 330Ci
E46 (99-05) > 330i
E46 (99-05) > 330xi