When does a Maximum Taxi Weight Restriction happen on a 737-800?
The Maximum Taxi Weight (MTW) is one of the weight limitations in the FCOM:


(Boeing 737-800 FCOMv1 L.10.3 Limitations - Operating Limitations - Weight Limitations)

It can be the limiting factor when the actual takeoff weight including required fuel is very close to the MTOW and adding taxi fuel would get you above this limit. Note that the difference between MTW and MTOW is only 500 lbs (about 2 hours of APU use or 35 minutes of taxi). If the required taxi fuel is higher than that (which can happen at a busy airport), you are limited by MTW.