People who are meticulous can be pretty annoying, what with their extreme attention to detail. But if that person is, say, your surgeon or your accountant, you'll want them to be meticulous.
The Latin root of meticulous is metus, which means "fear," so it's easy to see how eventually meticulous got its meaning. Someone who's meticulous is afraid of what will happen if they're not careful enough to get every detail right. "Detail oriented" and "perfectionist" are other ways of describing someone who cares deeply about the small things and about getting things exactly right, every time. Concert pianists must be meticulous, because audiences are always listening for wrong notes.