Large format basically means big film size cameras. These cameras use sheet film sized 4x5 inch or larger, such as 8x10 inch, but many can also use roll film. In photography, size does matter, as the bigger the film the better the quality. Larger negatives produce better quality prints because they require less magnification than smaller negatives. To make an 8x10 inch print from a 35mm negative you have to enlarge it eight times. With a 4x5 inch negative, it only has to be enlarged two times. An 8x10 inch negative doesn't need to be enlarged at all.
Large negatives also provide a greater range of tonal values and less graininess because of more silver halide crystals on the image. To do large film you can use various cameras, but for professional photography with digital cameras you need a precision model. This is because the darkening effect of the digital infrared filter gives you less depth of field. Large format cameras can be bought for less than $500 and can reach over $5,000.