Holbein the Younger was a man in demand once his reputation had reached a certain level and his early years in Germany were essential in developing his craft and also coming out from the shadow of his father. His connections in England would then grow at an impressive rate once he had moved across from Germany. Despite his connection to both of these countries, his style is considered most similar to the work of Netherlandish artists from this period. Jan van Eyck is perhaps the best example of this.
During the Renaissance portrait art was particularly popular and prominent. Landscape painting, however, was almost unheard of, particularly with regards the notion of having a scene entirely made up of natural elements without any figures at all. Without photography at that time, portrait paintings gave individuals an opportunity to be remembered by future generations in a visual form. The better artists would also be able to potentially tailor their depictions into a more flattering finish.
Word of mouth was the main promotional tool for artists of this era, sometimes as a result of people seeing examples of their work and on other occassions perhaps being introduced to the man himself. Holbein would become part of the political elite in England, an artist who became a tool for Henry VIII as he sought to woo a new wife on several occassions. Most monarchies vied to be considered the most culturally advanced and art was a major part of that.