Mindfulness is generally being aware of what is happening to your mind. It is being knowledgeable about your emotions, your thoughts, your body, your comings and goings. If you are mindful, it generally means you are self-reflective. Therapists teach mindfulness when they ask you about your feelings, and when you explore your history. The more you know yourself, the more you are mindful.
Concentration is placing attention on an object and not wavering that concentration. If you watch a television show and you pay attention to it the entire time, you have been concentrating on that television show very well. It is harder to concentrate on your breath, but it is still concentration.
Often mindfulness and concentration are confused. We think that we are not being mindful when we are not concentrating. While we might lack both concentration and mindfulness at once, it can also be true that we are generally mindful, but we lack the ability to concentrate.
While riding a bicycle through a park, it is somewhat silly to concentrate too much on one thing–there is so much happening. But we can be mindful of how we feel generally, that we going slow or fast now and then, that we are thinking about a topic that is important to us, that we are remembering a good friend, and that we may or may not do one more lap. Yes, we may not be concentrating on one thing, but we can be very mindful.