A gearbox bicycle is a type of bicycle that has gears inside the frame instead of outside on the derailleur like you see on most bikes. Think of the frame as a box, and inside that box are gears that help you change how hard you have to pedal. These gears are kind of like the gears in a car that help you speed up or slow down.
The cool thing about a gearbox bicycle is that it can make shifting gears really easy and smooth because all you have to do is use a little lever and the gears inside the box will shift for you. You don't have to worry about the chain moving from one gear to another like you do with a normal bike.
Also, because the gears are inside the frame and protected from the outside elements, they are less likely to get damaged and require less maintenance.
So, in simpler terms, a gearbox bicycle has gears inside the frame that help you pedal easier or harder without having to worry about a chain moving from one gear to another.