There are several main resorts in Tenerife. The first is near the airport in the South of the island, and is split into 3 areas, Los Cristianos, Las Americas and the Costa Adeje. This large resort attracts most of Tenerifes tourists, as the South gets the best weather and generally has nicer beaches than the North. Tenerife is a volcano and as a result it tends to be rainier and cooler in the North due to the winds, however it is windier (but sunnier) in the South. There is plenty to do in this area - a newly opened waterpark, Siam Park, is one of the main attractions and is much more impressive than anything found back in the UK. There are also a variety of tour operators that specialise in dolphin and whale watching.
The main disadvantage of Los Cristianos etc. is that the 18-30's flock there on lads holidays, and as a result the area has become slightly tacky. Drinks offers can be found in force, with a large array of bars and clubs perfect for youngsters. Gary Lineker's brother even owns a bar here and is one of the top draws come sunset - the creatively named Lineker's Bar.
The North of the island is slightly less developed, including Puerto de la Cruz. The town has a couple of decent black sand beaches - the main attraction here is Loro Parque, an impressive zoo which also has live dolphin, sea lion and killer whale shows - well worth a visit no matter what your age.
I would recommend getting a hire car if you wanted to explore the island, the best beaches are out of the tourist hotspots - for example Playa las Teresitas, just east of the capital, Santa Cruz (see photo below). Although the beach is artificial, it has white sand (imported from the Sahara) unlike the natural Tenerife beaches and is probably the best beach on the island, and rarely gets crowded.
Overall Tenerife has alot to offer - a trip up to the top of Mount Teide is a must as well - and is definitely one of the best holiday destinations for some winter (or summer) sun.