Thumbnail sizes is a built-in WordPress theme feature that allows theme designers and developers to define thumbnail sizes for images uploaded by the users. Often users confuse think that thumbnail sizes only apply to thumbnails or featured images. It is NOT true. Thumbnail sizes apply to any and all images that you upload in your WordPress. Thumbnail size is better defined as additional image sizes.
Designers and developers can choose to use one of the sizes defined in WordPress Settings » Media screen, or define their own additional image sizes. Once a new size is defined, WordPress will automatically generate a copy of each size when you upload the image. It does not automatically generate new sizes for previously uploaded images. However, there are plugins such as Regenerate Thumbnails that you can use to generate new sizes of all previously uploaded images.
There is some criticism of this feature. Critics say that this feature can consume a lot of hard disk space if you have multiple image sizes and a lot of images on your site. Unfortunately this criticism is accurate. If you have a lot of images, then you want to limit the amount of image sizes that you have on your site or simply pay for more web hosting space.