Networking leads to interviews because it makes you familiar before your resume ever lands in the application pile. Plenty of firms keep internal trackers where bankers log which students they spoke with, how the conversation went, and whether the candidate came across as prepared, normal, and genuinely interested in banking.
If you work your way up to Vice Presidents or Managing Directors, those are people with the ability to push a resume forward. Junior-level calls still count, though. Analysts and associates are frequently asked for input when interview lists get built, and a few positive conversations can be enough to get your name mentioned.
Some banks also lean on school teams or alumni groups to decide who gets interviewed out of a given university. A few analysts and associates who went to Cornell, for example, may end up reviewing the Cornell applicant pool. At those firms networking carries extra weight, because the person on the other end of your call may be sitting close to the decision.
The second payoff comes once you actually have the interview. Your answer to "why us" is far stronger when you can name specific people you spoke with and explain what you learned about the firm, the group, or the culture. That lands better than saying you like the bank because it is prestigious.