Telepresence allows developers to run microservices locally while still connecting to a Kubernetes cluster. It creates a bi-directional tunnel between the local development environment and the cluster. This allows the local process to access environment variables and DNS from the cluster pod. As a demo, the presenter shows running a front-end service locally using Telepresence while it connects to backend services in the cluster. However, Telepresence is still maturing and has some limitations like only supporting swapping one service and potential network and DNS issues.