These are typically used when blinds are installed on doors to keep the blind from moving all over the place (and getting bent up) when you open and close the door. They used to be used on every window years ago before air conditioning as people kept their windows open and it would keep the blinds from flopping around in a breeze or from the inward rushing air of whole house attic fans, used in older homes to get air circulation. Today hold down brackets are typically only used on doors.
An interesting aside of this is that homeowners would have to clean their screens which acted like a filter and trapped the dust and dirt, but also have to their blinds as well. When I first started selling window blinds in the latter 1970's, women we're resistant to them as they remembered having to clean them every year as kids and what a pain it was. They weren't taking into account that today they have air conditioning so it's no longer the problem it was.