A British aristocrat of Welsh descent he grew up in exile in Brittany having fled from the Yorkist Kings of England. As an individual with some claim to the throne (even a very vague one) he knew the Yorkist monarchs would want him dead.
After the failure of the revolt of his cousin, the Duke of Buckingham, Henry VII became the leading Lancastrian contender for the throne of England. He landed with a force in Wales and marched into England. There his Lancastrian forces decisively defeated the Yorkists under Richard III at the Battle of Bosworth Field in 1485. This victory ended the long running Wars of the Roses between the two houses. His claim to the throne was tenuous and based upon a lineage of illegitimate succession. However, Richard's claim to the throne was little, if any, better.
Principal to Henry's concerns on attaining the monarchy was the question of establishing the strength and supremacy of his rule. There were few other claimants to the throne left alive after the long running and bloody civil wars, so his main worry was pretenders such as Percy Warbeck who were backed by disaffected nobles. Henry succeeded in securing his crown by a number a number of means, but principally by dividing and undermining the power of the nobility. Other methods include his marriage to Elizabeth of York the leading Yorkist heir, an act that unified the warring houses. He was a fiscally prudent monarch who restored the fortunes of an effectively bankrupt exchequer by introducing efficient mechanisms of taxation. Royal government was also reformed with the introduction of the King's Council that kept the nobility in check.
His elder son Arthur having died in 1502, he was succeeded by his second son, Henry VIII. Henry VII did not want the negotiations that had led to the betrothal of his elder son to Catherine of Aragon to go to waste, so he arranged a dispensation for his younger son to marry his brother's widow -- normally a degree of relationship that precludes marriage in the Roman Catholic Church. Henry arranged a dispensation from Pope Julius II.