Some editors used them to help detect UTF-8 encoded files. Since they are also valid zero length space characters they also served as a nice easter egg for people who ended up editing their linux shell scripts with a windows text editor.

An attempt to store the encoding needed to decode the data with the data, rather than requiring the reader to know it somehow. Your program wouldn't have to care if its source data had been encoded as UTF-8, UTF-16, UTF-32 or some future standard. The usual sort of compromise that comes out of committees, in this case where every committee member wanted to be able to spit their preferred in-memory Unicode string representation to disk with no encoding overhead.

When UTF-8 was still very much not the default encoding for text files it was useful to have a way to signal that a file was UTF-8 and not the local system encoding.

Some algorithms can operate much easier if they can assume that multibyte or variable byte characters don't exist. The BOM means that you don't have to scan the entire document to know if you can do that.