What motivated western Europeans to explore and colonize in the wider world?

The desire for the products of far away places.

For example:
Spices from the East Indies
Gold from Central and South America
Fur and tobacco and fish from North America
Slaves from much of Africa
Space to settle away from crowded or unfriendly home nations (Pilgrims, Huguenots, Puritans, Quakers etc)
Desire to spread thir particular religion
I am sure you can find more in your text.

The motivation behind Western European exploration and colonization in the wider world can be attributed to several key factors:

1. Trade and Economic Expansion: The desire for new trade routes and the acquisition of valuable goods, such as spices, silk, and precious metals, motivated European explorers. The lucrative spice trade, in particular, was dominated by Arab and Italian merchants at the time. Europeans sought to bypass these intermediaries and establish direct trade routes to Asia, which would yield significant profits and enhance their economic power.

To understand this motive, you can delve into the historical events that led to the Age of Exploration. One significant event was the fall of Constantinople in 1453, which blocked the traditional overland routes to Asia. The Ottomans controlled these routes, making it difficult for Europeans to access goods from the East. This led Europeans, primarily the Portuguese and Spanish, to embark on maritime exploration in search of alternative routes.

For this, you might want to explore the role of key explorers like Vasco da Gama, Christopher Columbus, and Ferdinand Magellan, who undertook voyages to find new trade routes and expand European influence.

2. Competition and Rivalry among Nations: The period of exploration was characterized by intense geopolitical competition among European powers. Nations such as Portugal, Spain, England, France, and the Netherlands sought to gain an advantage over one another by establishing colonies and controlling key trade routes. The establishment of colonies became a means of projecting power, amassing resources, and securing advantageous trade relationships.

To grasp this motivation, it would be helpful to examine the geopolitical landscape of the time, including the Treaty of Tordesillas (1494), which divided newly discovered lands between Spain and Portugal, as well as the subsequent struggles for dominance between these Western European powers.

3. Spread of Christianity: Another significant factor was the desire to spread Christianity. Many European countries, particularly Spain and Portugal, saw colonization as an opportunity to convert indigenous peoples to Christianity. This religious motivation intertwined with their political and economic goals, creating a powerful driving force for exploration and colonization.

To grasp this aspect, you may explore the history of religious conflicts and the role of religious institutions during this period, including the Spanish Inquisition and the subsequent missions led by religious orders, such as the Jesuits.

By understanding these factors, one can gain insight into the motivations behind Western European exploration and colonization in the wider world during the Age of Exploration.