A proxy server is a computer with Proxy Software used on some corporate networks. It is used for all World Wide Web traffic, such as the viewing of Web pages. It can be used for the filtering of Web sites to prevent people from going to certain types of sites, but more commonly it is used on networks where there is not a direct connection to the Internet available for all computers (or where a direct connection would be too expensive).
In simple terms, Proxy server servers as a gateway to the Internet for a whole lot of computers connected through One phone line (could be normal dial up, or DSL, or leased line), like in an office environment. You will have a computer acting as the Proxy Server because that computer is connected directly to the Internet through the phone line and then you have other computers connected to the computer acting as the proxy server, which use the proxy server to connect to the Internet. That's all, Simple.
OK, now coming to your daughter's request.
1. If her school has blocked certain sites, it is for her own good, they would have blocked sites that are into pornography or sites that are not good for school children. It is illegal to install Proxy server software to bypass the schools laws. And they will come to know of it pretty soon. You are not doing the right thing by try to help her get a proxy server software.
2. What are they, I explained that in the beginning.