Fusional means that, in the morphological system of a language, a single wordform encodes multiple parts of the meaning in a way that is opaque and can't be predicted from the parts.

That's very abstract but an example makes it clear. Consider some Latin words with their English translations:

mensa -- table (singular, nominative)

mensae -- tables (plural, nominative)

mensae -- to the table (singular, dative)

mensis -- to the tables (plural, dative)

There are two parts of meaning (whether it's singular vs. plural, and whether it's nominative vs. dative) which are expressed in these forms, but the way this is done is opaque. You can't look at "mensis" and break it into a part that corresponds to plurality, and a part that corresponds to dative: the suffix -is conveys both of those features simultaneously. That's a fusional language.

Compare with the Hungarian equivalents: (Finnish is similar, but I know Hungarian and not Finnish)

asztal -- table (singular, nominative)

asztalok -- tables (plural, nominative)

asztalnak -- to the table (singular, dative)

asztaloknak -- to the tables (plural, dative)

Here you can identify that the suffux -ok corresponds to plural and the suffix -nak corresponds to dative. So the Hungarian paradigm here is agglutinative, not fusional. The upshot is that the Hungarian paradigm will be easier to learn and to extend to a very large number of cases compared to the Latin paradigm.

A simple web search can bring you to https://en.wikipedia.org/wiki/Fusional_language

>Another illustration of fusionality is the Latin word bonus ("good"). The ending -us denotes masculine gender, nominative case, and singular number. Changing any one of these features requires replacing the suffix -us with a different one. In the form bonum, the ending -um denotes masculine accusative singular, neuter accusative singular, or neuter nominative singular.