It didn't have any meaning before Julius except as his family's name. The Caesars were the line of emperors starting with Augustus and the title carried through the royal bloodlines, as it were, and later became synonymous with "emperor" hence Kaiser, Tsar and so forth.

I just wanted to note that technically, Julius Caesar was never a Roman emperor. He was declared "dictator in perpetuity" shortly before his assassination, but that isn't the same as the system of titles and accumulated power that we condense into the simplified term "Roman Emperor." Augustus established this system and his successors cemented it.

As the Patrician families grew in size, different branches needed ways to differentiate themselves. The Julii were an old family, and the tree likely had many branches. The hereditary cognomen became ways to distinguish these branches. Some were due to physical traits (there is one for being born with teeth), others were due to military triumphs (scipio africanus or pompeiius Magnus). I read somewhere (no source since its an old memory) that Caesar may have been ironic - meaning fair-haired and associated with a male line that went bald early in adulthood.

Caesar was a cognomen, a family descriptor. In this case the family descriptor was 'fine head of hair'.