You make two attacks against a single target. If you're wielding a light blade, spear, or flail, you get to make an additional attack (note that it doesn't say two attacks in the secondary attack section, like it does in the primary attack section) against the same (or a different) target.
Except you can actually take up to 4 attacks, assuming you hit with both initial attacks. see below.
Primary Target: One creature
Primary Attack: Strength vs. AC, two attacks
One target, two attacks. Clear as day.
Weapon: If you’re wielding a light blade, a spear, or a flail and have Dexterity 15 or higher, make a secondary attack.
If you're using a particular weapon, you get the secondary attack. Clear as day.
The "weapon" section of a power description modifies the immediately preceding "hit" "miss" or "effect" section (see silverstep for example). Therefore, the weapon section of Rain of Blows is a part of the "hit" section, which is applied each time the character hits with an attack roll indicated by the "Primary Attack" section. Thus, for each hit, someone with a light blade, spear or flail and at least 15 Dex gets a secondary attack.
The only reason anyone argues about this is because people think it is overpowered. It isn't unclear at all. If the power allowed two attacks against any targets (like twin strike does) and said "Weapon: If you're wielding a mancatcher, the target is immobilized", no one would argue that you only get to immobilize one target.