The definition, found in the Terminology of the Imperium section of the Appendixes of Dune, defines muad'dib thus:

The adapted kangaroo mouse of Arrakis, a creature associated in the Fremen earth-spirit mythology with a design visible on the planet's second moon. This creature is admired by Fremen for its ability to survive in the open desert. In addition to the markings on the second moon, there is also a constellation called Muad'Dib in the sky of Arrakis; its tail points to the north.

The second, Muad'Dib, is that by which he is known openly. Stilgar explains that the choice pleases them and then goes on to explain:

Muad'Dib is wise in the ways of the desert. Muad'Dib creates his own water. Muad'Dib hides from the sun and travels in the cool night. Muad'Dib is fruitful and multiplies over the land. Muad'Dib we call 'instructor-of-boys.' That is a powerful base on which to build your life, Paul-Muad'Dib.
Paul is reluctant to throw away his full past and get rid of the full name his father gave him, which is why he first wished to be called Paul-Muad'Dib. Unfortunately, this name was soon forgotten and became simply "Muad'dib". Also, it was hoped that by keeping the name his father gave him, he could prevent the mass slaughter that would occur later in his name. Sadly, it was not. The meanings of both Usul and Muad'Dib have powerful ramifications and a great deal of foreshadowing for the purpose Paul has on Arrakis.