What is a burner safety control issue? How do I go about fixing it. Thanks for any info.

More info needed, like the brand and model number of the furnace,, might be a limit switch, could be a flame senser

It's a slant fin furnace with a beckett oil burner. Model AFG.

Fuel oil units are risky enough for an experienced technician, downright dangerous for the ambitious D.I.Y.'er. I would strongly recommend that you let a pro handle it.