Assume for a moment that research output is affected by time in the field; either older people publish less due to resting on their laurels, or older people publish more due to greater experience allowing them to publish with less effort; I don't know without reading the paper which is true.

Now consider what happens if men are (on average) more experienced because up until recently more men entered the field than women, but then the trend reversed. If you just compared female to male research output you could come to the wrong conclusion; the difference in experience could overwhelm the difference between sexes.

So there are various statistical tools you can use to measure the difference due to experience, and subtract it out from the difference between sexes to get a more accurate measure of the difference due to sex. Doing this is called "controlling for a variable"

It basically means instead of measuring "papers published" they chose to measure "papers published per year"

No, they mean that they control for 'career length' ... e.g. an academic with 5 years of history is likely to have a better score than one with 2 years of history.

So they effectively compare women-with-1-year vs men-with-1-year, etc. etc, rather than 'women with h-index 5' vs 'men with h-index 5'

edit: should be "Women with h-index of X after Y years" rather than just "Women with h-index of X" (e.g. they control for Y years' publishing between men and women, assuming that time-in-academia is correlated with h-index. Quick glance at the paper suggests that time-in-academia has R2 of 0.62 with h-index)

Thanks. And what does the standard deviation 0.13 means? I just don't know how to interpret the result.