Picture Style is the "look" that the camera gives the video at time of recording. They are presets which vary saturation, sharpness, contrast etc.
Like shooting in jpg (unlike RAW) these settings are as the video is recorded so, for example, if your video is over sharpened there is little you can do about it. Similarly if you record with high contrast there is little you can do subsequently to open it out.
The camera has a number of picture styles loaded which you can swap between an also adjust yourself. A good original for video is Neutral with contrast backed off to -2. Cinestyle is a picture style developed be Technicolor which (theoretically) provides the best video for subsequently adding contrast, saturation and colour correction in post production without loosing clarity. See Chas' excellent thread on how to get and load Cinestyle and several other picture styles.
Magic Lantern is a firmware modification which gives you camera a great many more functions many of which are aimed at video. For example, it will give you meter bars on the screen telling you the sound level when recording video. It alows you to listen to the sound using the usb/av lead when recording. It produces many differnt metering graph inlays. It is also good for still photography as it gives you inboard interval timing and will auto ramp interval timing exposures to a set reference.
Saying it is a firmware modification sounds a bit drastic. It isn't, it's like either running Windows or Linux on your PC. You put magic lantern on your card (every card) and when the camera starts it boots up the software. To stop it you just put in a clean card without Magic Lantern.
