Implicit memory (also called "nondeclarative" memory) is a type of long-term memory that stands in contrast to explicit memory in that it doesn't require conscious thought. It allows you to do things by rote. This memory isn't always easy to verbalize, since it flows effortlessly in our actions.
Procedural memory is the type of implicit memory that enables us to carry out commonly learned tasks without consciously thinking about them. It's our "how to" knowledge. Riding a bike, tying a shoe and washing dishes are all tasks that require procedural memory. Even what we think of as "natural" tasks, such as walking, require procedural memory. Though we can do such tasks fairly easily, it's often hard to verbalize exactly how we do them. Procedural memory likely uses a different part of the brain than episodic memory—with brain injuries, you can lose one ability without losing the other. That's why a person who has experienced amnesia and forgets much about his or her personal life often retains procedural memory: how to use a fork or drive a car, for example.
Implicit memory can also come about from priming. You are "primed" by your experiences; if you have heard something very recently, or many more times than another thing, you are primed to recall it more quickly. For instance, if you were asked to name an American city that starts with the letters "Ch," you would most likely answer Chicago, unless you have a close personal connection to or recent experience with another "Ch" city (Charlotte, Cheyenne, Charleston…) because you've heard about Chicago more often. In the brain, the neural pathways representing things we have experienced more often are more salient than those for things with which we have fewer experiences. As with short-term memory, long-term memory can weaken with age or with cognitive conditions. For example, it can be harder to complete a procedure that was previously quite easy for you. You might forget a step to baking a cake you've baked a hundred times, and that you thought you had firmly committed to memory.