Plexiglas is a trade/brand name for
Thermoplastic Acrylic (other brands of acrylic include
Perspex,
Acrylite and
Lucite).
Plexiglas has better light transmission properties, and is also much lighter and tougher than the equivalent thickness of regular glass. While it's more prone to scratching than regular glass, such scratches are comparatively easy to remove, using very fine abrasives and polish.
Plexiglas can be produced via a process of extrusion, or casting. Cast plexiglass tends to be of a much higher quality, and contain less irregularities than its extruded counterpart. All acrylic will degrade under ultra-violet light, and should be specially coated before use in glazing applications.
It's important to remember that Plexiglas is a plastic, and not glass, and as such can be damaged by certain solvents. If you use a solvent-based cleaning product on Plexiglas, you're likely to be left with a smudgy irreparable mess.