Shades of Java...

What seemed to be an easy task did not turn out that way, kinda like my difficulty with the Java update a few weeks ago. I sucessfully downloaded what I thought was version 9.0.124.0. at this link. http://www.adobe.com/products/flashplayer/   But the successful install turned out to be 9.0.115.0, which is the one I already had. So I went to Add/Remove programs and got rid of 9.0.115.0 and tried to download the newer version again. It starts out OK, and I press the bar to allow the ActiveX control, and then I get a "Network Error--Please Check Your Internet Connection"...which is fine. This has happened twice in a row. Exactly what does this program do and can I safely do without it?