What power does house speaker have? Why is it noteworthy he's losing the vote? Why do they keep voting and over-riding/not abiding by the last vote?
The Speaker of the House is the top official of the US House of Representatives. They set the legislative calendar, decide the chair(wo)manship of the various committees, and are 2nd in line to succeed as President should something unforeseeable happen. They are (along with the Senate Majority Leader) in charge of what bills even make it to a vote in Congress.
The summary from wikipedia is "[t]he speaker is the political and parliamentary leader of the House and is simultaneously its presiding officer,
de facto leader of the body's majority party, and the institution's administrative head."
Becoming speaker requires a
majority * (not just plurality) of votes from members of the House. With the current House size set at 435 members, that means 218 votes are required. The Speaker has been decided in a single vote for all but 14 Congresses in US history. The most recent was in 1923 which took 9 votes, and the longest was in 1859 which took 44 votes over 8 weeks.
en.wikipedia.org
*This could be bypassed by agreement of the House. In some rare past Congresses, the House has agreed to let plurality decide. The other thing to note is that voting "Present" (or not being there to vote) actually lowers the "total vote" count; this means that for every 2 "Present" votes, the number of votes required to win decreases by 1.