There are many web services that allow users to upload pictures to a hosting site. The image host stores the images on its servers, and shows the individual different types of code to allow others to view that image.
Most of these solutions provide free storage space, with more features available if you are willing to pay for a premium account. However, there are problems with these solutions. Leaving aside privacy and ownership issues, these services typically do not provide good integration with other platforms. There is a simple alternative which gives you more control and flexibility – self-hosted open source gallery software.