The data itself of course will not physically move as datasets are regularly copied onto servers around the globe in order to ensure reliable service, regardless of geography. It is the legal responsibility for these bits that is moving and just as American food standards are less stringent than European ones, so too is data-protection law.
This means that digital giants can deploy AI such as face recognition with ease compared to a scenario that would see legal authority for the data behind the profile remaining in Europe. This is because anyone, regardless of location could bring a complain under European law but once we all accept the new terms, anyone in Britain will lose the protection of European law.
We will also see lobbying in Westminster from America's large tech companies following Brexit for favourable changes to our data protection laws.
This will, in my opinion at least, see data protection given a wider berth as access to a multitude of data points for AI adoption will be required as the AI revolution accelerates through it's gears.
Google and Facebook collect more data about what people are doing on the internet—the web pages they read, the services they use, the links they click—than any other companies. Those data are used to construct profiles of internet users, against which personalised advertisements may be sold. This year, as a consequence of Brexit, the firms are moving legal responsibility for that data from Dublin, where it has sat for the past few years under European law, to California, where both technology firms have their headquarters.