What is an electrical box?

It's a non-technical term, so it means whatever the speaker means. Most often they are talking about the box where the fuses are located.

An electrical box is what is behind an electrical cover plate. The box serves as a safety device to protect an area where wires are joined together. They can be made of metal or plastic and come in a variety of sizes nd shapes. There are many kinds of box covers, some for switches, some for electrical receptacles.

A fuse box or circuit breaker box is the central location where all the circuits are connected. Here, the circuits are protected from overload and can protect your home from electrical fires. Newer homes use circuit breakers rather than fuses.