PAC contributions allow individuals to circumvent limits on individual donations. So, interest groups can collectivize and use collective financial influence to support a candidate who might support that interest group's preferred policy.
Added wrinkles include how PACs are structure and how donations to PACs are reported to the FEC.
In short, however, interest groups use PAC funds to allow donors to band together to support a candidate with money at a higher rate than what is allowed for individual donors.