Rollout simply means rolling update of application. Rolling update means that application is updated gradually, gracefully and with no downtime. So when you push new version of your application's Docker image and then trigger rollout of your deployment Kubernetes first launches new pod with new image while keeping old version still running. When new pod settles down (passes its readiness probe) - Kubernetes kills old pod and switches Service endpoints to point to new version. When you have multiple replicas it will happen gradually until all replicas are replaced with new version.

This behavior however is not the only one possible. You can tune Rolling Update settings in your deployments spec.strategy settings.

Official docs even have interactive tutorial on Rolling Update feature, it perfectly explains how it works: https://kubernetes.io/docs/tutorials/kubernetes-basics/update/update-intro/