How are modes used when improvising on the piano?
Like the major and minor scales, each mode has its own tonal qualities - in fact, the major and minor scales are themselves modes (ionian and aeolian, respectively). By pairing certain modes to certain chord changes, you can create unique sounds. For instance, the chord progression C major - F major can be paired with a melody based on the major scale, but by using the Mixolydian mode you can make your music more bluesy. A minor chord progression will pair with Dorian mode to create a more modern, jazzy sound.
It really depends on what kind of mood you wish to create, and also what the other musicians you're playing with are doing. In a jazz trio, the pianist will play off of the bassline, but they'll both be paying attention to the chord progressions. There's a lot more freedom there than, say, an 18-piece big band where you're better off limiting your improvisation and letting the ensemble speak for itself.
What is so special about Miles Davis music?
Miles Davis' music influenced the world of jazz. His 1959 album "Kind of Blue" was a revolutionary step towards today's music: "The album's influence has reached beyond jazz, as musicians of such genres as rock and classical have been influenced by it, while critics have written about it as one of the most influential albums of all time." from Wikipedia. He composed many famous songs such as "Milestones" and "So What".
"Miles Davis is regarded as one of the most innovative, influential and respected figures in the history of music. He has been described as 'one of the great innovators in jazz'." from Wikipedia.
Although many like Louis Armstrong thought of Davis as someone who breaks all of the jazz rules just to be weird, Miles' new ideas and revolutionary improvising solos set a new milestone in the history of jazz. He is one of the greatest trumpeters of all time.