An inflecting language is language where the form of words change for grammatical reasons. In terms of typology, an inflecting language is opposed to an isolating or a agglutinative language because of an inflecting morphology: stem+affix (which doesn’t exist in isolating languages), with a certain type of irregularity in the inflection (contrary to agglutinative languages).

In French: cheval (singular of “horse”) / chevaux (plural), it’s impossible to find the suffix -s, usual marker of the plural form.

One of the common characteristics of languages considered as inflecting is the dynamic of “internal inflection” where inflection doesn’t consist in adding a suffix or a prefix but requires a sound change of the stem itself.

Thus, we’ve seen cheval/chevaux in French, which is an internal inflection, but we can also consider the verbal stem sing in English, which can appear as follows (I) sing (present), (I) sang (past), sung (past participle). We can also consider the pair man (singular)/men (plural). In both cases, inflection appears through a sound change, while modifying a vowel within the stem.

Latin languages such as French are usually considered as inflecting.

Note: The limits of morphological typology of languages distinguishing agglutinative languages from inflecting and isolating languages are often very vague. Those languages should be considered as “poles” towards which the morphology of a language is headed.

As explained before, no language is “exclusively isolating”. There are always a few inflecting characteristics. On the other hand, languages considered as “agglutinative” show, by definition, an inflection, but certain characteristics are usually more regular than for languages said to be “inflecting”.