Oracle is widely used because
1) it is a mature database. It offers more than saveing data relationally. It has significant backup/recovery protection for example. It is in fact all those things that you do not see that make is so great. I call it mature, some people call it industrial strength but you get the idea.
2) it is robust. For those who want to get into it, it is the most advanced database technology available. In the right hands one can do orders of magnitude more work with it than any other database.
For govt. use
1) it can be had cheap by the govt. (US anyway)
2) there is a specialized “secure” version for the US govt. and I am not aware of any other database that meets the requirements the US govt. put forth.