Imagehosting sites are hard to manage. I had one in past, I put Adsense ads on it, but, was forced to remove them because of 18+ pics being uploaded by users. And the 10 GB/day Bandwidth limit by my webhost was eaten up at an alarming rate.
Free imaging hosting sites usually made money from the ads they put around the images, hoping that some of their visitors clicks through the ads and makes a purchase or buy something, the same as affiloiates
popup ads and banner ads .. most of the image hosting website limit the bandwidth or allocate the disk space. If you upload more than 500 or 1000 files to their site then they will ask you money otherwise suspend your account.. So lose files or pay fees.
They can provide you with free image hosting but in the same time they are collecting database so in future they can upsell and crosssell you with others product. They can get huge database with free image hosting seem you knew that bandwidth is become cheaper and cheaper.
Its simple, they show Ads on their websites when traffic comes to their websites. Mainly they gain popularity for their websites from Facebook and Instagram. Even big brands like Pantaloons in India uses Facebook, Twitter for building reputation. If they have not done this then their investment in the business will have gone into bad debt many years back.
This image hosting websites normally earn from the ad sense on there sites some of the business pays this site post there advertisements. And also this sites not avail all the images as free products the post a single image as a free from a shoot and if a person needs another images from the bundle then he needs to purchase it.
I think they earn their money from Google Adsense ads. Free image sites get a lot of traffic on a daily basis. By having the ads strategically placed (right sizes, ad colors) they can make a really good income.
They earn money from the ads they display. I'm starting an image hosting site as an experiment using a VPS service that offers unmetered bandwidth on a 100M port.