Yes, thumbnails are automatically generated.
It is 95% certain your image is too “big” for your server to create a thumbnail. Note that “big” does not refer to the file size. To create a satisfactory thumbnail the original image, most likely a compressed file such as jpg/jpeg, needs to be uncompressed on your web server. A typical modern digital camera/smartphone image might explode to 30MBs when uncompressed, even though the file size might only be 2MB or less.
You should have an error message to confirm this is the problem (administration > site administration > logs – filter for “errors”).
Alternative causes can be linking to an external image or using a pdf file, neither of which can be converted to thumbnails. In these cases, you can include your own manually generated thumbnail copy at the same time you upload the original.