Surrending to the guru is giving up one's ego and attachments. It means letting go of all our neuroses and start a journey of basic sanity. Remembering that the guru is the doctor and we are the patient. Surrendering means just that, the wish to be "whole" (sain) and safe. Surrending is seeking protection from the guru, especially protection from fear at the time of death.
When we prostrate to the guru, we are actually surrendering. In our mind, we can say that we are surrendering, for example "I surrender to Guru". And when we get up, we should have the mind that wishes to benefit others. We should ask for the guru's blessings to benefit others.
Why do we want to surrender to the guru? Because he is the source of all our happiness. By following the guru's example, we can learn to achieve the same qualities and benefit others.