The active ingredients in Motrin and Tylenol are slightly different.  The acetaminophen in Tylenol can help with pain relief and fevers, and the ibuprofen in Motrin can help with pain relief as well as reduce inflammation and swelling (which Tylenol won't do). 

So, both will help relieve pain.  Both, to some extent will reduce fevers (though Tylenol is typically better in this regard).  Conventional wisdom in alternating is to get the best of both worlds - pain relief with fever reducing and anti inflammation properties. 

Care must be taken when alternating.  Doses must be correct, esp. for children, and ibuprofen cannot be taken as frequently as acetaminophen.   Overuse can damage children's kidneys, and while Tylenol has long been the standard for children, a pediatric pulmonologist in OH published a paper earlier this year outlining his reasons for avoiding the use of acetaminophen all together for children (links to the increased likelihood to develop asthma). 

Always consult your physician if you need detailed info or are looking for a course of action.

Just to amend this, the alternating of the two is usually only done when a severe fever and cold isn't responding to other measures.