In the case of stainless steel or other metal watch straps, they can be adjusted by removing links - which should be done by a professional and not yourself to prevent any irreparable damage to the watch strap and potentially the watch itself.
If you have a nylon, resin, or fabric watch strap, you probably won’t be able to adjust it. However, most watches are able to have the strap removed through little pins around the case. This comes in useful when you are not satisfied with the size of the watch strap, find it uncomfortable, or just want to change it.