“Orbitals” usually refer to 2-electron orbitals, and they are more stable (lower energy) than half filled orbitals (1 electron), since they have room for an additional electron— with no need for it to occupy another orbital which will have a higher energy level.
Thus, the new electron can have lower quantum numbers (or at least, lower-energy). a new electron in a half-filled orbital resides nearer the positive nucleus. The new electron gets a space at a lower energy level without having to find a new or with one or more higher quantum numbers. So (for example) the second electron in helium can still go into the 1s level of hydrogen, and doesn’t need to go up to 2s, and this is good.
When you say that “half filled orbitals” are more stable, you are really talking about half-filled shells or subshells— a condition in which a collection of orbitals with the same energy and angular momentum quantum numbers each contains one electron (where each has room for only two). Examples here would be chromium and manganese which both have five d orbitals half-filled, for a 3d5 configuration. In chromium one electron leaves the full 4s of vanadium to do this, so there are a total of six half-filled orbitals)
Here the extra stability is simply due to ability to spread electrons out in the maximum amount of space with the same energy and angular momentum quantum numbers. In the case of chromium, the extra space is so attractive that it pulls an electron from the 4s2 of vanadium (which is a lower energy level with a pair of electrons) because the opportunity to minimize electron-electron repulsion by half-filling the 4s and all of those 3d levels, overrides the energy to be gained by pairing at the lower 4s level.