Locke: If we need to change party members, I guess we'll just head back to Narshe...
Celes: So... how are we going to get there? The Empire's on the southern continent... They've closed down all the harbors, so there aren't even any ships sailing there anymore.
Locke: The town of Jidoor to the south is full of wealthy aristocrats... One of them might know a way in. "Where there's a gil..."
Celes: Locke.
Locke: Yeah?
Celes: Why are you coming with me?
Locke: Hmm? Well... there's the rumor about that legendary treasure being there and all... ...I just wanted to have a look around.
Once again, the poll was tied, this time for second place. Cyan secured his spot, but the last slot was tied between Edgar and Gau. And the coinflip went... to Gau. Dammit.
Anyway, I have the first four espers.
Espers do three things. First, they teach magic! Each esper teaches one to five spells, at different learning rates. Ramuh hear teaches Thunder quickly, Poison less quickly, and Thundara rather slowly.
Kirin teaches a few curative spells, such as Cure, Esuna, and Poisona -- Kirin's Cura is the slowest spell I can learn at this point, at only 1x modifier. Siren teaches Sleep, Silence, Slow, and Fire; all rather quickly at 5x or faster. Cait Sith teaches Confuse, Imp, and Float.
From here on out, battles will start giving magic AP. Multiply the magic AP earned after battle by the learning rate for any given spell, and the character will learn the product as a percentage of that spell. When it hits 100%, they learn the spell completely and can cast it forevermore.
So with those two AP, whoever has Ramuh equipped has (2 AP x 10 learn rate) 20% of Thunder, (2 x 5) 10% of Poison, and (2 x 2) 4% of Thundara.
The second thing espers do is boost character stats. Some espers have level up bonuses, giving a boost to strength, stamina, speed, magic, HP growth, or MP growth whenever a character levels up with that esper equipped. Ramuh here gives Stamina +1, Cait Sith gives Magic +1, Siren gives HP+10%, and Kirin gives nothing.
The HP bonus is based on what the character would have earned at level up, not their max HP. If Celes has 350 HP and would normally get 50 more at level up, equipping Sirens HP+10% turns 50 into 55 (add 10% of the gain), not turning 50 into 35 (adding 10% of Celes' maximum HP).
The last thing espers do is allow summon magic: characters can summon the esper they have equipped once per battle. Ramuh blasts enemies with electric damage, Kirin regens the whole party, Siren and Cait Sith silence and confuse all enemies respectively.