Unlike great britain, a significant motivation for spain to explore and colonize the so-called "new world" was

 To spread the power of the Catholic Church.

Explanation/detail:

The Requerimiento [Requirement] was a document written in 1510 by the Council of Castile (in Spain) which was used by the Spanish when they dealt with native tribes in the Americas.  Here's a bit of that document, which required the natives to convert and submit to the authority of the church:

On the part of the King, Don Fernando, and of Doña Juana, his daughter,  Queen of Castile and León, subduers of the barbarous nations, we their  servants notify and make known to you, as best we can, that the Lord our  God, Living and Eternal, created the Heaven and the Earth, and one man  and one woman, of whom you and we, all the men of the world, were  and are descendants, and all those who came after us.  ... Of all these nations God our Lord gave charge to one man, called St.  Peter, that he should be Lord and Superior of all the men in the world,  that all should obey him, and that he should be the head of the whole  human race, wherever men should live, and under whatever law, sect, or  belief they should be; and he gave him the world for his kingdom and  jurisdiction.   And he commanded him to place his seat in Rome as the spot most  fitting to rule the world from; but also he permitted him to have his seat  in any other part of the world, and to judge and govern all Christians,  Moors [Muslims], Jews, Gentiles, and all other sects. This man was  called Pope, as if to say, Admirable Great Father and Governor of men. The men who lived in that time obeyed that St. Peter and took him for  Lord, King, and Superior of the universe; so also they have regarded the others who after him have been elected to the pontificate, and so has it  been continued even till now and will continue till the end of the world.