It means some graphics person told them to get 300 dpi resolution images. Explain that any measurement "per inch" is for printing and does not exist in digital images -- there are a certain number of pixels in the image, not pixels "per" anything.
It's only when you translate pixels into a display format (monitor screen, printed page, pointillist oil painting) that a "resolution" of pixels in a given measurement makes any sense.
I might ask how large the images will be printed/displayed, and what the OUTPUT resolution and halftone screen will be (for conventional offset printing). If you are printing images on paper using a 150 lpi halftone screen, you want about 1.5 times (2 times maximum) the screen resolution, so 225 dpi images. Then, the printed size enters the equations. Say the photos will be printed 8x10 inches, you'd need images with 1800 pixels wide by 2250 pixels high.
Luckily, today's digital images have enough pixels for high-quality printing at fairly large sizes, and hard disks can handle gigabytes of data cheaply. It took a lot more planning and careful image-handling harder when disks and RAM were measured in megabytes.