In the United States at least, voter registration will include your place of residence which will place you in a specific precinct. In other words: "I am so and so, and I live here. Votes that affect this area include me, and I get a say."

When voters are voting for things, for example a tax levy to fund a new school, or for who will be their state or federal congressional representatives, it's important that the voters in that school district or in that congressional district are the ones voting for their representatives or for the bills or initiatives that affect them. This isn't quite as important for national elections, gubernatorial races, or for the senate at the federal level, but it's obviously incredibly important the more local you get.

Without voter registration, that model breaks down. Even mundane things like how much staff and equipment should be at a polling location is not easy to figure out when you don't know how many voters you'll have. If you haven't worked as a poll worker it's really enlightening to learn about how the process works and a great way to meet your neighbors.

One of the issues is that the US, unlike most of Europe, for example, doesn't require registering your address with your locality or police when you move.