The short answer is nothing much. The longer answer, is well, longer. If a motherboard is replaced with exactly the same model, revision and version or one previously it should work fine.
Variations may be introduced if you have update the BIOS of the previous board, or the BIOS was updated since acquiring the second. Windows won’t care about either of those unless the BIOS update allowed new features or new processor support needed to make yours work.
If both boards were acquired at the same time then there should be no issues with BIOS. While Windows “molds” itself around the motherboard it’s installed on, it has enough leeway to cope with many changes. Some drivers may be discarded, or requested by Windows, and you might be asked to insert the installation disk to load new ones, but Windows should cope.
In a like for like swap, only the MAC address of the on-board network device will change. These are hardwired Media Access Control addresses which are unique to each individual device. The address is a 12 character hex address that look something like 0C:A0:AB:12:C8:14. The first six characters are the manufacturer code and the last six is the serial number of the particular device.
When Windows Vista was first launched, there was a process where if the system changed in any way you had to revalidate it. Microsoft soon realized how unpopular this way and quickly scrubbed it. System builders, overclockers and other enthusiasts were forever having to ring up the call center and have the software revalidated. In the end, many acquired illegal cracks for their legitimate software to bypass this. That defeated the object of the feature and was abandoned soon after.
Windows can cope with a lot, including the swapping out of hardware without having to be re-installed. If the component is a major one like the motherboard, it is always advisable to load a fresh copy of Windows in order to get the most out of the system. This isn’t the case for a like for like swap. As there is no difference between the two components, Windows won’t even notice the change.