The executive branch of the United States government is a massive organization. The vast majority of all government workers are part of the executive branch.
The executive branch as a whole is under the supervision of the president. The president is the head of the entire branch. Under him (or someday her) are the cabinet secretaries. They are the heads of all the departments of the government.
Under the cabinet secretaries are all of the rest of the executive branch of the government. For example, all of the people who work for the FBI are part of the Department of Justice. Therefore, they are all members of the executive branch. As another example, everyone who works for the Internal Revenue Service (the agency in charge of taxation), is a member of the Department of the Treasury. The people who work in national parks are all part of the Department of the Interior. Even the military is part of the executive branch. They are part of the Department of Defense.
Thus, everyone whose job is in some way connected to carrying out federal laws is a part of the executive branch. That branch is the massive organization that is charged with executing all of our laws.