"Broccoli" was a nickname given to Lieutenant Reginald Barclay by Wesley Crusher. The nickname began as a form of inside joke at the expense of Barclay due to his perceived ineptness and nervousness. When Data found out about this, he didn't understand what Barclay had to do with a vegetable, of course, referring to broccoli.
After Captain Jean-Luc Picard inadvertently called Barclay the name Broccoli, Data attempted to excuse the faux pas, explaining that "Metathesis is one of the most common of pronunciation errors, sir. A reversal of vowel and consonant, "Barc" to "Broc"." (TNG: "Hollow Pursuits")