In political science, the term “hard money” refers to money that is (in the United States) given directly to candidates to use for their own campaigns as they see fit. This is money that the candidates will get to control. These are, for example, made into ads where the candidate explicitly appears and says “My name is X and I approve this message.” Hard money, then, is money that is directly given to candidates and which the candidates can use however they want. It is to be distinguished from “independent expenditures” which can be used to support a candidate, but which that candidate cannot control. Candidates cannot even coordinate their plans with people who do independent expenditures.
There are strict limits on how much hard money can be given to a candidate. Right now, for example, an individual can give a candidate $2,600 per election. For example, a person could have given Mitt Romney $2600 in early 2012 when Romney was running in the Republican primary and another $2600 after he won and was running in a separate election against President Obama.
The implication of hard money is that it is supposed to limit the influence that individuals can have on politics. The limits on hard money giving are supposed to prevent rich people from simply being able to buy elections or to buy too much influence over a candidate.