Money is tremendously important because money is needed for all of the ways in which candidates reach voters. If a candidate lacks money, that candidate will have a much harder time persuading voters to vote for them.
In modern elections, all forms of reaching voters cost money. The most high-profile way of reaching voters is through television advertisements. These cost large amounts of money to produce. It also costs a great deal to buy the airtime in which the ads run. However, even less high-profile means of reaching voters cost money. One thing that is very important in modern elections is identifying potential voters and contacting them. The actual contact does not cost all that much as it is typically done by volunteers. However, it costs money to figure out whom to contact. Candidates do not simply want to call everyone because they will be wasting their time and efforts. They will get a lot of people who are already guaranteed to vote for them or who would not even consider voting for them. So candidates spend a lot of money on technical consultants who use various kinds of data to identify voters who need to be called. Finally, candidates can reach out to voters by doing tours of states and trying to speak in front of as many voters as possible. This takes a tremendous amount of organization and costs a lot of money as well.
So, money is important in elections today because it is needed for all the ways in which candidates try to reach voters.