One person's complaint is easy to treat as a private inconvenience. A petition shows that other people are prepared to attach their names to the same request. It converts scattered agreement into something that can be counted, delivered, and discussed publicly.
The request matters as much as the signatures. “Improve our neighborhood” leaves an authority free to interpret almost anything as a response. “Keep the library open on Saturday mornings” identifies a decision that supporters can recognize as accepted, rejected, or still unresolved.
Support does not travel automatically into power
A group of residents could gather signatures for a safer crossing near a school. The list may help demonstrate demand, recruit volunteers, and secure a meeting. A formal petition system can add a required response or another procedural step, as in the UK Parliament's petition process. Those arrangements differ between institutions.
Signing is also a relatively small commitment. A petition with many supporters does not reveal how strongly they care, what alternatives they considered, or whether people affected by the proposal were reached. The wording can hide tradeoffs that appear only when implementation begins.
Its strength is making a request and its constituency legible. Organizers can then use the response to decide whether they have won a change, need a more specific proposal, or have found people willing to do more than sign.