What are motion graphics?
Motion graphics is a form of 2d or 3d animation based around moving graphics.  It can include such things as moving titles, animated presentations and graphs, animated background (motion backs), whiteboard animations, animated product demonstrations and more.

It can range in complexity from relatively simple (such as basic moving titles) to extremely advanced multi-layered projects laid out in 3d using numerous interacting objects.  Software such as Adobe After Effects and Apple Motion are often used for producing motion graphics.  It is also possible to produce some motion graphics in Adobe Flash, though it is more designed for pure 2D animations.  At the time of this writing, there wasn't much in the way of good open-source motion graphic software.

Motion graphics can be deceptive in the apparent simplicity when well done.  If you have no experience in the field, you should be prepared to encounter a lot of issues and challenges when trying to make a really good looking motion graphic.  It takes animation, graphic design and editing skills to produce a very high quality motion graphic and the tools themselves are complex beasts that can take a while just to learn the tool-set.

If you are looking for a professional looking motion graphic on a quick time table and you have no experience in the field, your best bet is likely to hire an experienced professional to do the work for you.  If you are looking to do it for your own purposes, it is an interesting field, but be sure not to set your bar too high.  Start simple and learn from there.  It is a field that can take months to years to get good in.