The Apex Scheduler runs an Apex class automatically at a set time: you write a class that implements the Schedulable interface, then schedule it with System.schedule('Job name', '0 0 7 * * ?', new MyClass()) or from Setup → Apex Classes → Schedule Apex. You stop it with System.abortJob(jobId) or the Del link on the Scheduled Jobs page.
I deployed a real scheduled class to a Salesforce Developer Edition org, scheduled it, triggered the two errors almost everyone hits, aborted it and ran its test class. Below is the code, the real output and the cron expressions you need.