Sometimes it means, "Able to work without someone looking over their shoulder at all times."
Sometimes it means, "Able to lead and mentor others."
And sometimes it means, "Has organizational skills above and beyond engineering skills, able to lead cross-team initiatives and deal with all the human/organization issues around the engineering."
The latter definition is the most interesting to me, it describes what "Staff" and "Principal" engineers do in most orgs. But if I had to pick a line to draw, I'd say that while a Staff or Principal spends most or all of their time working on projects that involve the human/organization issues around the engineering, a senior engineer is one who does this at least part of the time.
There are other, perfectly valid perspectives on what makes an engineer "senior," but what I like about this one that's relevant to TFA is that this kind of "seniority" is hard to fake.