what does it really mean?
That is both a simple and a complex question.
First, for the simple: it means something is moving back and forth around a central point or anchor, and can be
basically described by the mathematics here.
For the complex: when people use this term esoterically, they generally mean
quantum vibration. But they mix it up with the vibration we are more familiar with - mechanical vibration, especially sound. We speak of being "in tune" with someone when we are clicking with them. That is perfectly fine as a metaphor. But our minds are not vibrating in any meaningful sense other than the pulse of blood carrying oxygen to our neurons.
The quantum world is quite different form the world we perceive, despite the fact that the world we perceive is made up of particles that exist in the quantum domain. Because all those quantum effects are in random directions, and they cancel each other out as you scale up your statistical mechanics. For example, it is quite possible that a single electron in an oxygen atom in your lung could remain "attached" to that atom and briefly appear somewhere near Mars, only to come back near the oxygen nucleus in your lung a moment later. Mind you, that would be exceedingly unlikely, but it's still allowed under the rules of Quantum Mechanics as we currently understand them.
That's quite weird and wonderful, and one of the things that got me interested in Quantum Mechanics when I first encountered
Pauling and Wilson's book back in high school.
But all the electrons in your body won't do that at the same time, leaving you to blow apart in a gooey residue of positive charge. While still allowed under the rules of QM, the probability of that happening is now in the realm of that plied by Zaphod Beeblebrox in the Heart of Gold. Because each atom in you is doing its thing independently.
But then people who are not technically proficient, the kind of people SOT described as having a kindergarten level of understanding (too true), are claiming just that when they point at some improbable woo doctrine and then justify it with "because, quantum!"
So now we get to vibration. There is vibration on the quantum level. You can think of the bonds between atoms as tiny springs in certain respects. When those springs absorb light of the proper energy, they start to bounce back and forth like a spring with a weight on each end and can be described with
math very similar to the kind you encountered as an undergrad in your Physics and Differential Equations classes if you were a techie like me. Light of higher energy (visible, UV) will cause the electrons in the bonds to jump around and light of a lower energy (microwave) will cause the molecules to spin (rotational quanta), but infrared light is exactly the right energy to make individual molecules go "boing".
But just as all your ground-state electrons won't find Mars at the same time, all the vibrations in your body are going every which way and cancel each other out. You don't have a quantum vibrational state as a macroscopic being. You do have a
mechanical fundamental vibrational frequency, but that is not what these woo-loons are talking about. If someone talks about your "vibrational level" and upon questioning doesn't know how IR light works into this (and doesn't explain why their vibrational theory seems unaffected by oh, say proximity to a friggin'
campfire), they are almost certainly pulling stuff out of their posterior orifice.
I hope I didn't make your eyes glaze over, happy to say more if I was unclear.