Would be grateful if anybody could explain what splash damage is and how it works. Many thanks.

Basically, here's how it works:

If, in a skirmish of a battle, you are using a card that gives you a splash damage ability, then if you were successful against that unit (his unit was destroyed in that skirmish), your opponent chooses one of his other remaining units to destroy, once all of the skirmishes are complete. Your splash damage ability will say "ground", "flying", or "ground/flying", which indicates what types of units can be affected by the splash damage. Keep in mind, too, that if you are playing with the Brood War expansion, heroes cannot be destroyed by splash damage, so a different unit would have to be destroyed, if possible. Splash damage still happens if during the attack volley both units were destroyed in a skirmish. Splash damage does occur cross-skirmish, which means that even though a unit survives an individual skirmish, it might still be destroyed by splash damage before the battle is done.

NOTE: Health and attack values are not factored in when resolving splash damage.

TIP: When you are attacking an enemy and you think that he may play a splash damage ability against you, try your best to take other units along with your attack that would not be targeted by your opponent's splash damage. This is a great way to effectively nullify that advantage if played properly.

TIP: If you play it well, you could destroy a very strong unit with splash damage, even though you would not have had enough attack strength to destroy that unit by itself.