Mesquite is very hard and very dense, burns hot as can be, and is mainly used for grilling in Texas, although some do smoke with it. It has a very distinct flavor and smell unlike other hardwoods, and you can actually smell a restaurant burning it while driving by on the highway.
Mesquite is my favorite wood of all time for grilling red meat like Fajitas or Ribeye's. Super-hot fire for a short period of time equals great flavor.
On the other end of the spectrum, use too much Mesquite in your smoker or smoke with very green wood and you will never forget the taste (In a bad way!). Kind of like getting sick on Tequila, the memory lingers for years....Don't ask me how I know!