There are two apps in my update section that I did not install and I want them gone. 1 says it has mature content, what the heck is this?

press and hold app until they all start to wiggle. A red x will appear in top left corner of app, tap x to delete. The press home button.

Be careful not to judge a book by it's cover. Many apps are required to display the mature content warning simply because the access the internet. Two examples are Yelp! and Google, not typically "mature" apps.

Web browser apps display the same warning - and as Rkedge pointed out - any app that accesses web content may show that warning.

Atomic, Mercury, Google Chrome, iCab Mobile ... All web browsers and I think that they all display that same warning.