What does taking the Oath of Office mean to the Members-Elect of the U S House of Representatives?
There is a difference between what the oath of office means in technical terms and what it means to each member-elect. The first is knowable, the second is not.
Article VI of the Constitution of the United States says that members of the House of Representatives (and the Senate) have to swear an oath to support the Constitution. What this means is that a person cannot officially be a member of the House of Representatives until he or she swears this oath. What the oath means in technical terms, then, is that the people who swear it go from being members-elect to being actual members of Congress.
As to the more personal meaning of the oath, that is something that differs from one member to another. Most members surely see the swearing of the oath as a very serious and momentous thing. This is particularly true when they are first elected to Congress. There will be those for whom it has particular meaning because they feel that the US government has moved away from the Constitution and they feel that they will bring it back. Each member surely has a different set of meanings that they attach to the oath of office.