What is the advantage of the two-column journal format?

There's a widespread belief that shorter lines (fewer characters per line) are easier to read, because the eye doesn't have to move as far horizontally from the end of one line back to the start of the next. The left edge of the text (assuming left-to-right languages) may already be in your peripheral vision. Thus it's easier to visually find the correct line to read next, and avoid accidentally rereading the same line or skipping lines.

This is the justification for the extremely wide margins that LaTeX uses by default in one-column styles, for instance.

I don't know offhand if there is research supporting this belief, but maybe someone can fill me in if they know.

Two columns makes it easier to have short lines, without resorting to small paper size, large font sizes, or huge margins. Thus you still get a high density of text per page, and it keeps page counts down (and the associated costs).