DPI, MB and Colour Space - sorted
Searching the web for '72 vs 300dpi' and 'what's the best image size for Retina screens' will give you a headache, so I've done that for you and added a few things from my personal experience as a pro photographer.
DPI (dots per inch) or PPI (pixels per inch) is ONLY FOR PRINT. 'PPI' is actually the more appropriate term.
For web/screen the DPI/PPI is meaningless, the important thing is PIXEL DIMENSIONS.
For example 1500x1500px square image is ideal for most web use, unless it's for a full bleed/full width page banner in which case 2500px wide is the minimum.
See below for an example of the same image output at 72, 300 and 1000 DPI. Do you see any difference?
You can download them to check yourself in photoshop. They are all 1500px x 1500px and 782kb.
When printing images you should check with your print service and use their spec. If necessary go back to your photographer or designer and ask for the image output in the correct PPI and colour space. You'll often be able to preview the colour profile in Photoshop if you have a properly calibrated screen. CMYK Colour spaces should only be used for print, if you upload a CMYK image to the web you'll see some very strange colours. For the screen, it's RGB or sRGB.
When using images on the web, it's all about pixel dimensions. Retina screens and other higher resolution monitors require images with higher pixel dimensions to look sharp. That is why you see so many fuzzy images logos - people have not updated their websites and spcial media accounts.
MB size is not necessarily an indication of image quality. MB size is determined by the amount of colour data in the image and the pixel dimensions. For example a full colour landscape photo will be larger in MB size than a cutout of a white teapot. See below examples, same pixel size at 1500x1500 but very different MB size.
So next time someone asks you for an image 'at least 2mb' you can explain why that's not always required.
I always output my images at 300dpi so my clients can use on web and print.
How sharp an image appears is also determined by how far you are standing away from it - it's relative. For example an image on a magazine page needs to be a higher PPI than a billboard. To test this, walk up really close to a billboard or even a poster and compare to a magazine.