What does it mean when my service stability,abs and traction control light come on in my 04 Cadillac DTS

if trouble light on have vehicle scanned most auto stores offer service for free --the code will direct you towards repairing the problem which can be abs sensor --speed sensor to possible short in harness

problem usually narrows down to abs system problem or hub failing causing problem with abs --have vehicle scanned for the trouble code it will assist you as where to start in repairing problem most auto stores offer this service for free --in the mean time pull the abs fuse so brakes can revert to a normal non abs system till repairs can be made

The light being on means the system has detected a problem in one or more sensors. The vibration is the ABS modulating the brakes to prevent skidding because it has detected a wheel that is locked up. That wheel is most likely the one sensor that is giving you the error.

probably a wheel speed sensor or wiring

The stability control system is typically triggered by the abs system/connector sensor on your wheel hub bearing. If you haven't replaced your hub bearings on the front you may have one going bad. Cheap fix for a diy.

Chances are you have a wheel speed sensor that is not reading correctly.

have the OBD codes read as will pinpoint the faulty sensor/switch , will save you time and money trying to trace fault blind

take out the part you have fitted and have the OBD codes cleared ,then refit the part and see if the same happens

bad wheel speed sensor