Until 1824 presidential candidates were nominated by congressmen in an informal political meeting called a "caucus" (a favorite political term of John Adams). The caucus is still used today at some political conventions. As a presidential candidate in 2008, [[Barack Obama]] did better than [[Hillary Clinton]] in states that used caucuses (rather than an election by voters), which enabled Obama to defeat Clinton for the Democratic nomination despite Clinton having defeated Obama in many states that used open primaries. But in 1824, all the leading candidates for president were from the same political party (the Democratic-Republican Party), and everyone who was nominated by the congressional caucus was on the ballot on Election Day for the millions of voters to decide.
Jackson won more votes from the public than Adams on Election Day, but not a majority of the Electoral College votes as required to choose a president. The Electoral College is the system set up by the Constitution whereby special "Electors" from each state cast their ballots for president based on how the people of their state voted, and a candidate must win a majority of the Electoral College to be elected a president. That minimum number required to win a presidential election is 270 Electoral College votes today.
When no one wins a majority of the Electoral College, as happened in 1824, then the Constitution requires that the election go to the House of Representatives, for it to pick a winner. There Clay apparently struck a private bargain with Adams, whereby Clay persuaded congressmen to vote for Adams, and Adams, after he won, appointed Clay to be Secretary of State. Supporters of Jackson ("Old Hickory") harshly criticized this as the "corrupt bargain." Jackson, campaigning four years later against this "corruption", then crushed Adams in the next presidential election in 1828.