So far I have seen Attack, Move, Hold, and Arcane abilities. Some, like Move, are pretty obvious, but what is a Hold ability? What kinds of things do the ability types matter for?
So, for the most part, these don't matter. Also, for the most part, it's pretty obvious. Attack abilities are, well, Attacks. Move abilities are, well, abilities that move your character. Hold abilities aren't really the most well labelled, but essentially, the label is applied to any ability that neither causes you to move, nor attacks an opponent. This includes most self buffs, healing abilities, etc.
The one exception, as you may have guessed by now, is Arcane abilities. The main reason this matters is because of the Abjured condition. While under the effect of this condition, a character suffers a -2 penalty to all Arcane checks. What's an Arcane check? Well, it's any check involving that character being the user or target of an Arcane ability. As for what makes an ability Arcane - for the most part it's flavor; anything of a 'magical' nature, such as, for example, most Runecaster abilities is Arcane. As for why abilities like the Truebows Focus are considered Arcane, this is because of the way buff duration is handled in Conclave - every turn, a check of increasing difficulty is made to determine whether the buff fades - in the case of Focus and other Arcane buffs, that check is affected by the penalty from Abjured.
More details on how the check system works, including the aforementioned buff retention check, the Conclave Quick Reference is a really good read.