That symbol on a unit means that the unit has an ability that targets something, and therefore might have to pay extra if that something gains resist, or can't target a thing if that thing is invisible or untargetable (unless you have a detector or tower). Also, if a targetting ability is used on an illusion, the illusion is destroyed.
Many spells also target, as do many hero abilities. Interestingly, there are spells that affect specific units/heroes but don't target (like Chaos Mirror) and won't pop an illusion or incur resist surcharges.
It is weird, though, since I can't think of anything that affects targeting of bases... Mind-Parry Monk only affects effects that target units/heroes. I agree that it does seem unnecessary. Anybody else have any ideas of a time when a base's being targeted would matter for game purposes?
It is somewhat consistent, though. Pirate-Gang Commander gives units a targetting ability that also can only target bases, and Bugblatter's ability targets as well. The PGC ability is particularly weird, since it "targets," but there is no choice to be made: it always targets all opponent bases.
Extra weird: Firebird does not target (and therefore can't pop illusions) when it does 1 damage to every unit and hero the opponent controls. So why does it not target, while PGC's granted ability does target (each opponent's base)? Shuriken Hail is similar to Firebird.