If you make a new character, the only thing he can do is attack with the default weapon attack. So that is what a default weapon attack is; it is the sword icon that starts out on your left click.
There are 3 skills that are also default weapon attacks: Cadence (Soldier), Fire Strike (Demolitionist), and Savagery (Shaman).
When it says “activates off of default weapon attacks”, that means that it has a chance to happen every time you use a default weapon attack (normal, Cadence, Fire Strike, or Savagery).
So if you have 25% chance to use a WPS, let’s say Markovian’s Advantage as an example, then every time you attack (with default, Cadence, Fire Strike, or Savagery), you have 25% chance to use Markovian’s Advantage.
I hope this helps!
Also, there is one special case you should know about. Cadence does bonus damage every 3rd hit, and no WPS can activate on that 3rd hit.
So if you have 25% chance to use Markovian’s Advantage, and you are using Cadence, your attacks will look like this:
Normal (with 25% chance of Markovian’s Advantage)
Normal (with 25% chance of Markovian’s Advantage)
Cadence’s bonus damage (with 0% chance of Markovian’s Advantage)
Repeat.