Current is so high the contacts "weld" closed. Usually caused by cranking with a low battery or bad connection in starter circuit (heavy wire circuit between battery and starter THROUGH start relay/solenoid).
Karl
I second CrossBolt's analysis and suggest the following:
1. Battery should be tested /replaced. Can be charged on the bench then hook up and turn the scooter on for 30 seconds but don't crank the engine, turn off and test voltage with a multi-meter the voltage should read at least 12.3v (full charge a good battery should read 12.5v). I have found the GV / People 250 need a strong battery that cranks the engine rapidly or the scoot will have trouble starting.
2. excessive cranking damaged the solenoid and or starter relay. I suspect this is the real culprit across brands and scooters and motorcycles. In 90K miles of riding since the late 1980's I have never replaced a motorcycle starter or solenoid. I got my 2005 GV 250 with 2500 miles now I have 19K - no problems with the starter.
3. Kymco Rear brake light - watch out for this. As the scooters age 6 years + regardless of miles. The contact on the rear brake light switch corrodes. If you don't see your rear brake light come on when you squeeze the left brake light - the scooter will not start (verify that your rear brake light works and that the bulb is ok). Note: the motor will crank even if the lever is not pushed or with the kick stand down but it will not start. I took my switch apart and cleaned it and applied dielectric grease. It works great but sometimes still acts up. Quick temp fix is to press the lever a bunch of times.
4. Moral of the story: With 19K miles my scoot starts instantly when cold. Below 45 degrees and in damp weather I need to hold the starter for up to 6 seconds before it starts. In hot weather or when the motor is hot the choke does not come on and that requires throttle open ~ 1/2 way. If after cranking for 6 seconds stop and fix the problem don't keep cranking of you risk damaging the starter or solenoid.
5. Get help from your car: Hook jumper cables and then try starting - that ensures your battery is not an issue. If it starts right up your battery is weak and needs to be replace. I discovered this last year - scoot haveing problmes starting. After sitting a few days I noticed it cranked very slowly - replaced battery problem solved.