If someone is trainable, they can be taught or educated. People without work experience may be hired anyway, if the employer thinks they're trainable.
Your puppy is terrible on a leash and chews on shoes, but she's trainable. In other words, with enough consistent practice, you can teach her how to be a very good dog. And even though you've never set foot on a boat, if you want to learn to sail one you're definitely trainable — all you need is the right instructor. Trainable comes from the verb train, to "teach or discipline."