Networking leads to interviews because it makes you familiar before your resume enters the application pile. Many firms keep internal trackers where bankers note which students they spoke with, how the conversation went, and whether the candidate seemed prepared, normal, and genuinely interested in banking.
If you network your way up to Vice Presidents or Managing Directors, those people may have the ability to push your resume forward. Even at the junior level, several positive calls can help because analysts and associates are often asked for feedback when interview lists are being built.
Some banks also use school teams or alumni groups to help decide who gets interviewed from a specific university. For example, a few analysts or associates who attended Cornell may help review the Cornell applicant pool. At those firms, networking is especially important because your calls may be with people who are close to the decision.
Networking also helps once you get the interview. Your answer to "why us" is much stronger when you can mention specific people you spoke with and explain what you learned about the firm, the group, or the culture. That sounds more credible than saying you like the bank because it is prestigious.