Fuerteventura is all about surfing. You won't find an inhabitor of the island (who are called 'Majerero's') that doesn't surf, windsurf of kitesurfs. Everybody has a dangerous level of stoke. The islands' name already says it: "fuerte" translates to "strong" and "ventura" to "wind".
The different spots of the island also have to be explained. So here it goes.
Flag beach: easy spot, cross shore, nice swell, can be crowded, huge beach.
El Cotillo: advanced spot, cross shore onto huge stone walls, huge incoming walls of waves which have to be crossed to kitesurf, not crowded - but don't go out alone!
Faro de Tóston: intermediate spot, on shore, beach/reef break, can be crowded
El Buro: lays 5 minute drive south of flag beach, intermediate spot due to more swell, cross shore, not so crowded, more constant winds than flag beach.
Sotavento: probaly the most popular spot everybody knows, when the wind is 14 knts up north it can blow 25+ knts at this spot, cross offshore with rescue services, flat waters and a lagoon (check tides), awesome spot to go to when the wind up north is down.
La Pared: located near Sotavento, absolute advanced spot with big swell, reef break, don't go in alone, amazing beautifull spot.
Puerto Lajas: intermediate spot, cross onshore, crowded under locals, nice swell for kickers.