Mindfulness and meditation are very similar in that they both aid in quieting the mind. Meditation is often used as a relaxation technique to help with stress-relief. There are varying forms of meditation, including guided meditation, breathing meditation, mantra mediation where you chant a specific word, phrase, or prayer, and many others.
Mindfulness is not necessarily used for relaxation but it can be relaxing. Mindfulness is used to help our minds cut through the noise (thoughts and feelings) so that we can focus and concentrate on a given task and stay grounded in the present moment. The task that we are involved in may or may not be relaxing. For example, we may be practicing mindfulness while walking our dog. The practice of mindfulness in this task may be to experience the sensory experience of walking outside, the sights, sounds, smells. As thoughts arise we acknowledge them and let them pass by, we return to our present task. This example could be very relaxing. Another example of practicing mindfulness may be while we are in front of an audience of 500 people giving a speech. Mindfulness in this instance would be awareness of our emotion, thoughts, and physical experience while standing in front of a crowd of people. As these thoughts, emotions, and awareness of our physical experience arise, we acknowledge them and let them pass by, we return to our present task of giving our speech and connecting with our audience. This example is not necessarily relaxing.