3d10 means a creature gains hit points from 3 dices, each with the "size" 10.
So the DC for antagonize for this privateer would be 13.
Hit Dice, or HD, is equivalent of levels for player characters. You know how you roll a die each time you level up to gain new HPs? That's a hit die. A wizard gains d6 each level and a fighter gains d10, so while a third level wizard has less hp than a third level fighter both have 3 HD. And a multiclassed fighter 2 / wizard 1 would have 2d10+1d6, which is still 3 HD.
Monsters skip levels, but still have hit dice. As you can see, a dire bear has 10 HD and a dryad has 6.
Okay, so as I expected. But what about monsters, which have + bonus to HD? Is this bonus counted too?
The bonus is just a constitution modifier and similar stuff.
My 3rd level fighter with Constitution 10 has three hit dice and 3d10 hit points.
My 3rd level fighter with Constitution 16 has three hit dice and 3d10+9 hit points.
My 3rd level fighter with Constitution 16 and Toughness has three hit dice and 3d10+12 hit points.