Excellent question my friend. Which means I had to look up the answer.
Nation Influence
Influence as a nation is determined by how long you’ve been in a region. You can increase your influence by having WA endorsements. Influence was added to the game to prevent a nation that just moved to a region from taking over the WA Delegacy and immediately banjecting (Eject & Ban) every native.
The nation influence ranking system is:
Minnow
Vassal
Truckler
Handshaker
Duckspeaker
Envoy
Diplomat
Ambassador
Auxiliary
Negotiator
Contender
Instigator
Dealmaker
Enforcer
Eminence Grise
Powerbroker
Power
Superpower
Dominator
Hegemony
Hermit
…with Minnow having the least influence and Hermit having the most. When someone has access to the Regional Controls, they can calculate the “cost” to their influence for using those buttons. If they lack sufficient influence, the buttons don’t work.
BTW, Eject means you wake up in The Rejected Realms but are free to choose to return if you like. Eject & Ban has the same outcome, but you are banished - cannot return - until the delegate or founder decides to remove you from the ban list.
Influence has been a hot topic on NS Forum “Boo Hoo You Wrecked The Raiding Game” threads.

AFAIK, there are still plenty of active raiders with plenty of spunk left in them. They raided The Rejected Realms and kicked Kandarin out of the delegacy recently, which is no little feat. Some folks who don’t like influence are really saying is that they don’t like it when Founders turn off delegate access to the Eject and Eject & Ban buttons in Administrative Controls. This only only possible in User Created Regions that have Founders. It’s not possible in The East Pacific, because feeders have no founder.
To raid a region with an active Founder who has turned off delegate access to Administrative Controls is a silly thing to do, because all that happens is that you annoy the locals and get banjected. Seizing the delegacy accomplishes nothing.
So be nice to Lady Edea or she can banhammer you. The rules allow anyone with access to Regional Controls who has sufficient influence to banject (Eject & Ban) any nation for any reason, including just because they think they’re annoying.
The check on any delegate or founder who uses the banject buttons too frequently is social. We “vote with our feet” in NationStates and you can flee a region whose leadership is dumber than advertised and move your nation to a place whose leader you like better. We are vexed by awful rancid aspic (AKA adspum = recruiter advertisements) on our RMB because those recruiters hope that you’ll do exactly that.
Region Power
Regions themselves have power (I called it influence before and that was incorrect - influence refers to nations, power to regions), rated from Low to Extremely High. I could speculate on how that is determined, but I really don’t know.
Perhaps some veteran players here can explain it to us. It appears to be a combination of factors, like how long the region has existed, how many nations are in it, the total population of the region in citizens (a measure of how long the players have been in the game), how many of nations are in the WA, or even how active the region is in voting in the WA. I dunno.
There’s one guy I know who might have some insight. I’ll ask him and check back here if I learn anything new.
UPDATE
In the absence of a better explanation, the best speculation I have heard is that Region Power is the sum of the influence of all resident nations. What remains unexplained is how power might decline as a region shrinks or loses WAs - and if power does decline, how fast changes take place.
