Dear Student,
The answer to your querie is as follows:
The area of cross-section of a wire need to be uniform beacuse if there is a change in area of cross-section of the wire, there will be a proportionate change in the resistance of a wire as resistance depends on the cross-sectional area.
As Resistance(R)=ρL/A., hence R is inversely proportional to the area of cross-section and hence if the area of cross-section is not unifrom then there will be change in the resistance of the wire.
Owing to this reading of the meter-bridge experiment to determine the unknown resistance will have error, hence the cross-sectional area of wire throughout its length must be uniform.
Regards