dark boots
The short definition of Innocence has been provided in the Universe part. While activated, Innocence will be a weapon to fight the akumas. Basically, there are two types of Innocence: Parasitic-type and Equipment-type.
Parasitic-type Innocence takes form as a part of the user's body, like Allen with his left arm and Krory with his teeth. You can't part with it because it's a part of your body—they integrate in a cellular level. In short, the user himself has become the weapon. Quite saddening, but that's pretty much the truth. This type of Innocence consumes much more energy, so the user has an obvious different level of needs for food... this explains why Allen always eats a whole lot.
As for the Equipment-type, the name says it all. It has a form of an "equipment", something that you can wear, bring, or even drop. For example, Kanda's Innocence, "Mugen", is in the form of a katana. When the Equipment-type is broken, it will take some time to be repaired.
dark boots
"Land, ocean, and skies... Her legs take her anywhere. Surely, they will take her to a wonderful future as well."
Name: Dark Boots
Type: Equipment
Power: They enable her to become swift in almost every situation. It can perform extremely high jumps as well. The Innocence of Steel, Dark Boots.
Lenalee's Innocence, "Dark Boots", is an Equipment-type Innocence. While deactivated, it has the form of a pair of regular shoes. Lenalee puts them on everytime, although it is actually a burden for her.
"My legs... they feel so light. I suppose it's because I'm not wearing my Dark Boots. But my legs don't hurt at all. Those shoes were always so heavy... It always hurt." —Lenalee in chapter 140
Great power comes at a heavy price. I guess it's probably more than a proverb for Lenalee, at least when the Innocence is inactive. However, when the Dark Boots are invoked, the Innocence increases speed and strength on her legs. Therefore, like butterfly, she can move and fly around freely with those shoes.