During government shutdowns, many government employees are furloughed without the promise of back-pay. They're essentially jobless without income.
Senate and House of Representative members are considered "critical", therefore they cannot be furloughed during these times, even though they're the ones that ultimately pass laws to prevent the shutdown (or fail to).
This petition will give Senate and House members more incentive to reopen the government, or preventing shutdowns altogether, by stopping their paychecks during government shutdowns. They won't be furloughed, but they won't get paid either.