Foreign policy.
"Throughout his reign Henry's foreign policy was defensive: he reacted to external events in order to secure his Crown and dynasty." (John Guy, Tudor England.)
England was not a major player in Europe, although she was not insignificant. English woollen cloth was the best in Europe (how the mighty are fallen), and as a result, England had major trading links with the Low Countries, the Hanseatic merchants, France and Italy.
Edward IV was on good terms with Burgundy (being brother-in-law to the Duke of Burgundy), and managed to wangle a pension from France in return for not invading (1475). Edward did not really do foreign war, which was a Good Thing, as war was expensive. He did make sure, however, that foreign powers would not threaten his crown.
The exiled Henry Tudor found a home first in Brittany and then, when Edward succeeded in getting him chucked out, France. Christine Carpenter says that his foreign upbringing affected his ruling capacity, but that's another issue. Anyway, Henry certainly had a good idea of how important it was to stay on good terms with foreign powers.
Henry's foreign policy can be summed up by a memorable acronym - FARRTS.
Finance
Avoid war
Recognition
Reputation
Trade
Security
The major treaties that you need to know.
Holy Roman Empire
Brittany