As is the case with many terms, the word governor has changed throughout history. In the fourteenth century, the name described a prince, administrator, or other local official empowered on behalf of the monarchy to manage an area. In early times, a governor retained the powers of legislative, judicial, and executive branches. A good example is the feudal lords. The monarch would designate authority to feudal lords to manage a region on behalf of the monarchy. How the feudal lord managed was never questioned as long as the appropriate tribute flowed into the monarch's coffers. Feudal lords made laws, acted as judges, and enforced the laws. In this instance, a person can make the case the governor's role crossed all three branches.
In American history, governors appointed by the King of England had enormous discretion and power to manage a territory. It is not an understatement that a great deal of animosity that leads to the American Revolution was a response to the unchecked power of appointed governors in Colonial America.
In modern times, the word governor refers to a person in charge of the executive branch. In practical terms, governors do not have authority in matters of the judicial or legislative branch of governing. There are state and federal constitutions that delineate the powers of the governor from the legislature and courts. The role of the three branches and the checks and balances severely limit the governor from overstepping their role as head of the executive branch.
On the other hand, philosophically a person can argue that governors do expand their roles to cross into the legislative and judicial branches. The legislature makes the laws, but it is up to the governor how to interpret and enforce the law. Governors appoint judges, and it is not an unusual practice for a governor to appoint a judge representing a similar legal disposition to their own. Governors can claim a state of emergency and mobilize significant amounts of resources without the vote of the legislature or consultation with the judicial branch.
Though an argument can be made the position of governor crosses all three roles in government, in modern times, it is a philosophical argument at best.