The basic answer to this is that it is simply the surname. The British Monarchy is currently the house of Windsor. Queen Elizabeth's surname is Windsor and this will remain the case for at least the next three generations of Monarchs as all the first born children are male.

But down the millenia, there are a few reasons why the house name has changed.

The house of Windsor was created somewhat artificially by King George V who was the king during the First World War. His actual surname was Saxe-Coburg Gotha. So before the house of Windsor it was the house of Saxe-Coburg Gotha. This house became so when Queen Victoria married Prince Albert of Saxe-Coburg Gotha (he was Austrian) and her son Edward VII was of that house, and his son (George V) as well. George V thought his surname sounded a bit too German and changed to something more English to promote morale during the war. They have been Windsor ever since that Royal decree.

Referring to a Royal family as a House goes back at least to Saxon times, though they wouldn't necessarily have referred to themselves as such at the time. Historically its useful to divide peoples into groups for the sake of providing a narrative that's easy to follow. I'm not that knowledgable on the saxon times but a further run down of the British monarchy since the Norman invasion of 1066:

The house of Normandy began with William the Conqueror (William I), and includes his sons William II and Henry I. After that Stephen of Blois (somewhere in France) came over and claimed the throne, a nephew of Henry I, as Henry's son predeceased him. So he is in the house of Blois.

After Stephen, Henry I's grandson through his daughter became King, Henry II. His father was Geoffrey, count of Angou and so Henry is known as the House of Angou (also the Angevin line or Angevin Kings). His son's are also considered house of Angou (Richard I & John).

Thereafter, John's son (Henry III, crowned 1215) and the line that followed (Edward I, II, II, Richard II, Henry IV, Henry V, Henry VI, Edward IV, Richard III, Edward V) are known as the house of Plantagenet. Its not until the 15th century that the term Plantagenet was actually taken on as a family name, but historians have labelled the Kings from Henry III onward as Plantagenet to mark the shift in power base. You see, the name Plantagenet actually was coined in reference to Henry II, but his power base was vast and sprawling through Europe (plus we've already seen that he was the Count of Anjou). John lost all these lands and the power base was, from then on, England. Hence the noted shift in the "House" name from Edward I on. Its a useful differentiator.

The Plantagenet line lasted until the end of the Wars of the Roses in 1485 when Henry Tudor took the throne. His surname was literally Tudor so it was obvious that the House of Tudor had arisen. The house of Tudor was Henry VII, Henry VIII, Edward VI, Mary I, Elizabeth I.

As Elizabeth died with no issue, the crown passed to her cousin, James Stuart, and so the House of Stewart. Charles I, Charles II, James II followed.

William of Orange (Denmark) then shared throne along with his wife Mary Stuart, hence the house of Orange. They died without issue and Mary's sister Anne, daughter of James II became Queen so the House of Stuart was restored. The next monarch was George of Hanover (due to a religious dispute which resulted in the exclusion of Catholic monarchs). Hence the House of Hanover: George I, II, III & IV, William IV and finally Victoria.

This ties us up to where I started.

EDIT: Updated as I originally made a couple of omissions in the narrative (Queen Anne & James II).