The answer is etymology.
Many English words are built from a stem and some prefixes and suffixes. (I think this is true of most languages.) There are many suffixes that preserve the core idea of the word, and give it a particular grammatical nature and a particular meaning. For example, from the stem defin-, you can build the verb define (to give something a definition), the noun definition (the act of giving something a definition, or the outcome of this act), the (uncommon) noun definer (someone or something that defines), etc.
Many of these stems, prefixes and suffixes existed in ancestor languages of English. Many of the resulting words existed in ancestor languages, and sometimes different words in the same family evolved differently.
The examples you give are quite illustrative. The verb define comes from the Latin verb definire, and the noun definition comes from the Latin noun definitio. The verb combine comes from the Latin verb combinare, and the noun combination comes from the Latin noun combinatio. Note how one pair has the infinitive verb ending in -are and the noun ending in -atio, and the other pair has the infinitive ending in -ire and the noun ending in -itio. What happened here is that the ending of the verb was eroded: Latin verbs had over a hundred different endings depending on the mood, tense and person, whereas English has 5. Many verb endings got simplified to -e (often in French before they reached English), which erased the previous vowel. So what happened isn't that defin- got the suffix -ition and combin- got the suffix -ation, but rather that defini- and combina- both lost their ending vowel.
Although many stems of this type end with the vowel -a or -i, Latin also had the vowel e, as in. delere, which gave the English words delete and deletion through a less direct route). Some stems had no final vowel, e.g. cedere (many forms of the verb, including the infinitive, have an additional -e- to ease pronunciation), giving cede in English, and the associated noun cessio (whence cession) where the suffix and the final consonant had merged together and diverged already in an ancestor language of Latin.
The suffix -tion to form a noun from a verb, meaning the action itself or the outcome of this action, was very common in Latin (shown in the form -tio above, but the -n was already present in some cases) and in French (also spelled -tion) but it is no longer productive in English.
English has many other suffixes, some of them productive, most of them not. Most of these suffixes come from Latin, often through French, even though English is primarily a Germanic language. The reason for this is historical: German was the language of ordinary people (who mostly use existing words to designates objects from everyday life), French and Latin were the languages of learned people (who invent new concepts and make up words for them).