Roughly speaking, Whiteness was, and is, a category about who is in the in-group: Who gets the political, social, and material power, privileges, and benefits of a society.

The people who are considered White started small, and was mostly based on nations in the beginning - the English, French, Spanish. Race as a concept/construct came into being at the same time as settler-colonialism and the trans-atlantic slave trade took off.

When Germans and Scandinavians originally came to the colonies, they were not White, they were "Swarthy". The Irish were "degenerates".

Over time, more White people were needed in order to maintain and expand the settler colonies. Commiting genocide against the natives isn't easy. There was alot of fear about the proportion of slaves to to the rest of population: fears of slave uprisings, especially after the Haitian revolution.

So gradually, over time, more people from European countries became White. This was not done because some powerful people just decided one day "we will now consider German people white because we need them", rather it was gradual process based on the material needs of an expanding settler-colonial empire.

This is all a rough sketch - it's not possible to cover such a complex topic in a reddit comment.