Creature Ability List
From the comp rules glossary:


  
  Text on an object that explains what that object does or can do.
  An activated or triggered ability on the stack. This kind of ability is an object.
  


Every item of rules text in the text box (the box in the lower half of the card) is an ability. Doesn't matter whether it's keywords or full statements; static, triggered, or activated. In addition, lands with a basic land type have an implied ability: "T: Add 1 [color] mana to your mana pool."

In handwavy terms, "lose all abilities" means "pretend there's nothing printed in the card's textbox".

More precisely, you apply effects that add or take away abilities in "timestamp" order. So, for example:


I have a Stampeding Rhino. It has one ability: trample.
I enchant my Rhino with Trollhide. This gives my Rhino a second ability: "1G: Regenerate this creature" (the ability is printed on the Trollhide card, but it as an ability that the card gave to the Rhino).
My opponent plays Turn to Frog on my Rhino, which includes the text "loses all abilities". My Rhino now has no abilities, until end of turn. Both the Rhino's built-in trample and its enchantment-granted regeneration are removed.
After my Rhino is turned into a Frog, I activate Alabaster Mage to give it lifelink until end of turn. Now my Frog has one ability: lifelink.


(Power/toughness-modifying effects are actually a bit trickier, since they are applied in layers. So the Frog is 3/3, not 1/1. That's a different question.)