what is style.css?ver=1 tag?

To avoid caching of CSS.
If the website updates their CSS they update the ver to a higher number, therefore browser is forced to get a new file and not use cached previous version.
Otherwise a browser may get a new HTML code and old CSS and some elements of the website may look broken.

Adding '?ver=1' makes the HTTP request look like a GET query with parameters, and well-behaved browsers (and proxies) will refuse to cache parameterized queries. Of course well-behaved browsers (and proxies) should also pay attention to the 'Cache-control: no-cache', 'Expires', 'Last-Modified', and 'ETag' response headers (all of which were added to HTTP to specify correct caching behavior).

The '?ver=1' method is an expensive way to force behavior when the site developer doesn't know how (or is too lazy) to implement the correct response headers. In particular, it means that every page request is going to force requesting that CSS file, even though, in practice, CSS files change rarely, if at all.

My recommendation? Don't do it.

The purpose of the ?ver=1 is to parameterize the css file, so when they publish a new style.css file they up the version and it forces the client to download the new file, instead of pulling from the cached version.