Soft money is no longer nearly as important in American government and politics as it once was. The McCain-Feingold campaign finance law that was passed in 2002 banned the giving and use of soft money. Then the Citizens United Supreme Court decision of 2010 made soft money somewhat irrelevant anyway.
Before 2002, there were strict limits on how much money could be given to a candidate to use on his or her campaign. However, there were no limits on how much money could be given to political parties for generic “party building” purposes. As long as the money was not used on ads saying “Vote for X” for example, it could be given in unlimited quantities. An example would be a rich person giving $5 million to the Republican Party and the party using it to pay for efforts to “get out the vote” and for ads promoting Republican ideas (but not individual candidates).
This soft money was widely seen in those days as a bad influence on politics. It was seen as a way for rich people to have too much power in the political process.