To be very brief, it was not a reference to an empire as we moderns would interpret it. The statute was referring to an empire in the ancient Roman sense; a distinct kingdom of its own, ruled solely by its head, without influence from other kingdoms. This was an important legal distinction to make because the king could claim the right of total sovereignty over his people. As the king of an independent empire, Henry VIII would have no duty to respect the wishes of the Catholic church, the laws of which he was attempting to legally bypass.
In this context 'empire' means a polity where ultimate authority flowed from the head of the polity itself, not from an outside figure (the Pope).
There seems to be some historical controversy over whether the statute was using 'empire' in a novel way to describe a new kind of political arrangement (a kind of proto sovereign national state), or whether it was just used for its rhetorical power. For example here's an excerpt from one such debate:
"We differ here over whether the Act of Appeals abolished papal jurisdiction in virtue of the principle that in an empire (such as flowed from the king. England) spiritual and temporal jurisdictions It is not, of course, in dispute that the intention and effect of the Act was to make the crown the head of the spiritual jurisdiction in an unprecedented way. I have merely argued that "empire" provided no justification for this. Dr. Elton has contended that the Act used the term in a novel way as a territorial unit and invested it with a new sense, a superiority in spirituals. It must be admitted that Henry himself wanted to use it in this latter sense. But elsewhere imperium was consistently limited to temporal authority and it is doubtful whether its territorial shift in meaning." (Harriss & Williams 1965)
In any case:
"Even those who refuse to view the Act of Appeals as the moment of the definitive reinterpretation of the term "empire" admit that it was indeed Henry's aim and expressed wish to imply in its application to England that England was a sovereign polity separate from the rest of Christendom.52" (Greenfeld 1992, p. 51)
'Empire' seems to have been used in various ways in medieval Europe (as is described in the 'A Revolution in Tudor History?' debate I referenced above), but the meaning intended in the statute is that of 'the highest authority' (which originally applied to the Roman empire, and in this period most notably applied to the Holy Roman Empire). An empire is the only polity that could be argued is not subordinate to the Pope, unlike Kingdoms, Duchies etc.