The phrase actually means 'everything is o.k.' and it dates back to 1887 when Arthur James Balfour gained an unexpected promotion in government, to the highly ranked and important post of Secretary Of Northern Ireland. The apointment was made by his uncle, Lord Salisbury, who'se Christian name was Robert. People of the time, suspecting a probably justified dose of nepotism behind the appointment were wont to tease the new Secretary by winking, and advising 'Bob's your uncle!' hinting that it was through this family connection that Balfour got the job.
The phrase has since passed into common usage to mean 'everything is fine'.