Could be both matter particles and light from stars hitting the warp field and doing unpredictable things. When we've seen the ship slow from warp, some but not all of the trails resolve into stars, so this seems OK.
I hope it is permissible to quote Dr. Schneider at ex-astris-scientia.org:
Whenever a Star Trek ship is at warp, it seems that always several stars are flying by when looking at the main viewscreen or out of a window. The effect was probably created only to suggest the high speed of the ship. It is quite obvious that these "star streaks" can't be actual stars, because even at high warp a ship would pass by only one or two stars per hour but definitely not several stars per second. Here "passing by" means that the relative angle changes by more than 90 degrees, resulting in such an effect like the "star streaks".
We have to find another explanation for the phenomenon, and one may be Tcherenkov radiation. Similar to the sound cone as produced by a supersonic aircraft which overtakes its own sound, a starship moving faster than light would create a sort of light cone. At least the shape of such a cone would exactly match the paths of the star streaks which always emerge radially from the center of the screen or window. Maybe parts of this cone would be visible from inside the ship as streaks for some reason. Another, even simpler explanation may be that interstellar particles glow because of the friction with the field created by the navigational deflector.