They didn't take any other of the Atlantic islands close to Africa or Europe, and I'm no farmer but this place (I'm on holiday in Tenerife) looks pretty arid
Edit: "islands" plural
In 1402, French adventurers Jean de Bethencourt and Gadifer de la Salle, who were nobles who owed allegiance to King Henry III of Castille, started conquering the islands. They wanted land. They got it. Bethencourt got the title "King of the Canary Islands", though he was still an under-king to Henry.
It took the Castillians until 1495 to finish conquering the islands. (They were also claimed by Portugal for a while).
In the early days of Spanish control over the Canaries they became one of the world's largest sources of sugar (Maybe the largest). Sugar was very valuable. Eventually, the Caribbean islands became bigger sugar producers than the Canaries.
The Canaries were also a key stop on the Spanish galleon route from Spain to the New World. Ships would stop there for water and provisions, as the islands were on the best (due to the prevailing winds, not the most direct) route from Spain to the Caribbean.