What does |0> mean? ie what does the | > mean/do?
| > is just a decoration; it makes something look different. It's no different than when you put a little arrow over your vectors, or little hats over your unit vectors.
Ah, right. I thought it was maybe linked to < > meaning expectation value.
Well when you take the inner product of <x| with |x> you get <x|x>, which is a number and can be thought of as an expecttion. So the notation ("Bra and ket") isn't entirely arbitrary.
[itex] |0\rangle [/itex] stands for the ground state for a quantum system (the state with the minimum possible energy). The [itex] |\rangle [/itex] with "something" in between the vertical line and the angle means that the "something" is a "ket" vector.
Separate names with a comma.