Cypress agent is the tool that runs the tests. When the agent is configured to run test in parallel, it tries to connect a remote dashboard to coordinate the tests running order.
Parallelizing cypress tests means running different tests on multiple cypress agents at the same time. The official Cypress documentation greatly explains why is it good.
Sorry cypress replaces the original cypress dashboard. You will still need to set up (and pay for) a CI environment that runs cypress agents.
When using sorry-cypress you'll need to override the default configuration to set an alternative URL for contacting the remote dashboard.