The canonical examples of fusional languages are Latin and German. Most European languages are relatively fusional. Esperanto, which is a construction language based in part on many European languages, is a particularly clean and simple example of a fusional language.
A good illustration of fusionality in language is the Latin word amo, "I love". The ending -o denotes indicative mood, first person, singular, present tense. Changing any of these features requires replacement of the suffix -o with something else.