The Increment is the sum of all completed backlog items at the end of a Sprint, combined with the increments from all previous Sprints. Every Increment must meet the Definition of Done and be in a state that allows release. The Increment is the concrete proof that the team has created value.
In practice, each Increment builds on the previous one. After Sprint one, there is a working login function. After Sprint two, login and search work together. After Sprint three, login, search, and filtering are integrated and usable. The critical point is that the Increment must be functional at all times, not only after an integration phase at the end of a project. This forces teams to work in small, self-contained steps and deliver continuously.
The Scrum Guide defines the Increment as one of the three Scrum artifacts alongside the Product Backlog and Sprint Backlog. Whether the Increment is actually released after each Sprint is a business decision, but the technical capability to do so must exist.