I'm still an outsider when it comes to Valyrian, but this I can answer.
In English you usually have a rather definite "word as is" and then you can inflect it by adding suffixes. For example, you have walk, and you can inflect it walked or walks or walking. Sometimes there's something happening at the boundary between the suffix and the main body of the word, but that's small stuff. In languages that are heavier into inflections, things are not necessarily as crisp. There may not be any definite "word as is". You always use an appropriate suffix, and the suffixless body of the word (stem) isn't necessarily even pronouncable - it might end in a big consonant cluster that needs to be followed by a vowel. In these kind of languages a dictionary builder has to choose either to offer bare stems, which are not words as they are ever used, or to choose some inflection. For many languages, infinitive is the best choice for verbs. It's not the most used verb form in practice, and it's not necessarily the simplest, but it tends to have two really cool characteristics:
1) Infinitive often stands apart. There can be a huge number of verb conjugations in tense and person and whatever, but infinitive is often just one form of the word.
2) Infinite is the verb form that is used when the verb is not further defined by sentence (pretty much when it's not predicate). However oddly inflected the verb is, in infinitive it's still in sense "the word as is".
So: -agon is the suffix for valyrian infinitive verb form.
