CSS3 (https://developer.mozilla.org/en-US/docs/Web/CSS/CSS3) is the latest of the Cascading Style Sheets (CSS) specification. It adds support for media query, animations, flexbox, round corners, and a lot more. CSS3 makes it possible to natively animate elements, apply special effects, apply filters, and so on to get rid of the many JavaScript hacks that were used earlier.
Flexible Box, or flexbox, is a layout mode (https://developer.mozilla.org/en-US/docs/Web/CSS/Layout_mode) that can be used instead of the box model used traditionally. This allows having a flexible box model making responsive layouts easier to handle without floats and margin collapse issues.