Regeneration is a combat stat. It heals your creatures after you fight with them. Some creatures have it naturally, others may need to borrow yours via influence.
Energetic immunity is a stat that buffers against the negative effects of walking. In particular the higher your EI the less VE you lose by walking in places other than your homeland (doesn't work for No Man's Land citizens).
Trade sense is a stat that buffers against shop prices. The higher your trade sense, the less WI you need to buy armour.
Briskness will increase the amount of heat you can harvest with your Erolin Device.
Initiative is a combat stat. It determines which creature will move first in a battle.
Defence & Attack are interlinked combat stats. If my creature has 10 attack and yours has 2 defence, my creature will do 8 damage to yours (if it uses the "damage" ability).
Power is both a combat and non-combat stat. Mostly it's used to influence creature abilities such as heal, lifesteal, martyrism. Outside of combat it can also influence some spells.
Luck is both a combat and non-combat stat. In combat it will randomly affect your creature's performance, usually helping in an unpredictable way. Outside combat it can give you little surprises sometimes just for walking along.
Volition is gained simply by walking. Gaining more of it has no direct effect as of yet, though it's a good way to compare who has moved around more in the past.
Cartography lowers the AP cost of moving between scenes. If a scene costs 50 and you've got 40 cartography you'll still need at least 50 AP to move there, but it will only cost 10.
The following are stats related to resource gathering, or some to crafting. As far as I'm aware they all do the same thing but for different resources. The more of a particular resource-related skill you have, the more efficiently you can use the tool that lets you gather that resource. Some are easier to guess what they're for than others, but I'll leave it to you to figure out which is for what. Some stats cover multiple tools or activities.
All information is based on my own incomplete knowledge, so feel free to correct me.