Similarly, we can understand anti-bonding orbitals by looking at other ways the atomic orbitals can combine. Anti-Bonding orbitals are essentially the "opposite" of bonding orbitals. They are formed when atomic orbitals combine in ways that lead to predominantly destructive interference. The key feature of anti-bonding orbitals is that the molecular orbitals have a higher energy then the corresponding atomic orbitals. Thus the molecule (the atoms separated by a particular small distance) has a higher energy than the separated atoms (atoms separated by a large distance) and the atoms would prefer to be in the lower energy atomic state.
Another characteristic of anti-bonding orbitals is a "node" or place of zero electron density between the atoms. The higher in energy the MO, the more nodes it will have. In general, anti-bonding orbitals have higher energy and more nodes than their bonding counter parts.
We denote anti-bonding orbitals with a * symbol. Thus if someone is talking about π* orbital they are referring to an anti-bonding orbital. Below is a diagram showing the formation of an s-to-s anti-bonding orbital. Note that the orbital has a nodal plane between the two nuclei.
So anytime two atomic orbitals combine to give a lower-energy bonding orbital, an analogous higher energy anti-bonding orbital is also formed. Below is a figure depicting this simple bond/anti-bond molecular orbital diagram that we had for hydrogen. The diagram also shows that electrons (in this case) completely fill the bonding orbital and leave the anti-bonding orbital empty.
A common question is why would "anti-bonding" orbitals exist. In some ways this is a complicated question, but in others it is quite straightforward. When combining atomic orbitals there will always be two ways in which we can add up the atomic orbitals (remember they are just mathematical functions). They can add such that there is constructive interference. This leads to bonding orbitals. Or they can add up such that there is destructive interference. This leads to anti-bonding orbitals. When we are making MOs for molecules with lots of atoms, there are lots of AOs. This means that there is only one orbital in which all the AO add up constructively. However, the lowest energy MOs (the bonding ones) will have more constructive interference and the higher energy MOs (the anti-bonding ones) will have more destructive interference.