The phrase suggests someone is always readily available to assist or serve another person whenever asked. As the newest intern, I was at everybody's beck and call in the office.
Pro Tip 2/3
Potentially Negative
Used to indicate that one's time is heavily controlled by someone else, which can sometimes carry a negative connotation of subservience. She felt frustrated being at her partner's beck and call all the time.
Pro Tip 3/3
Not Literal
The phrase is figurative and doesn't mean one's presence is literally demanded; it's about being heavily relied upon. Even on his days off, the chef was at the restaurant owner's beck and call.