What conditions caused Europeans to undertake a dangerous voyage and settle in an unknown and dangerous wilderness?
Since you use the word "settle" I assume that you are talking about actual settlers like those who came to Jamestown and Massachusetts rather than those who were simply exploring, like Da Gama and Columbus. If so, there were a variety of conditions that caused them to leave Europe.
- Economic hardships. For many, there was a lack of economic opportunity in Europe. Things like the enclosure movement in England pushed people off the land, and there was generally not enough in the way of land or jobs for people in many parts of Europe.
- Religious differences. The Puritans, for example, had ruled England for a while but had lost power. They left in order to start a new polity where they could rule.
- Ambition. This is an economic reason, but one for the higher classes. There were those who had good lives in Europe but wanted more.
- Politics. There were some (like Scots and Irish) who wanted to come to America to be more free from the rule of England.
In general, then, people generally left Europe in the early days of settlement for either economic, political or religious reasons.