Child is the more politically correct term, though GED remains in common parlance and usage.
They are powerful psychics born with golden eyes (always the same base shade, but can look darker or lighter depending on the light) who can slave a type of pokemon to their will. IE: Dragon, Fire, Grass, etc. This is, in essence, mind control of a pokemon.
They also have limited telepathy and some have demonstrated being able to heal pokemon to a degree. The telepathy is limited in the sense it's limited to pokemon, possibly extending to people, though no-one is really sure how that works, because it does differ from GED to GED. There are also conflicting reports of what, exactly, a GED can truly do outside control pokemon. The terrifying thing about them is once a monster's slaved to their will, it takes a Darkened to break that connection, and the stronger the GED is, the stronger the Darkened must be.
Until they awaken, it is not known what type of GED they are, though it is possible to 'guess' or have psychics confirm (often Seers or psychometrics), given the child may gravitate to things that broadly reflect the type they'll be able to control. However, without a Seer or Psychometrists help, this is not a sure-fire way to tell and most consider it to be superstition at best and type casting at worst. (Word of Author: This is true, but also a very, very broad strokes and is never obvious, even in hindsight, though people will claim it is.)
GEDs awaken anywhere between the age of four to seven, and always under times of great stress and danger to themselves or immediate family. Depending on what they've been told, it can be a terrifying and frightening time when, very suddenly, the pokemon they want to stop is now obeying them. Depending on how powerful the GED is, the higher up the 'evo-chain' the first slaved pokemon is. The average GED will slave 'first-stage' pokemon on Awakening. To slave a 'final-stage/adult' pokemon typically indicates at least a class 3 GED.
GEDs are classed 1 to 4, with 4 being once in a century. Class 1 and 2 are the most common, yet there is some overlap between the classes. The downside to this is that the more powerful a GED, the more likely they are to be targeted for kidnapping by people who'd seek to use them in some manner or fashion.
One of the most powerful GEDs known to date is Dark-type GED Amy Yaeger (Ayumi Yoshida) who slaved a lv 68 hydregion. In-universe, this is a heavily guarded Orenjin Clan Secret and it's said that the Clan that guards her has, as of 2012 already taken out several threats to the preteen's life.
There are darker sides, of course. To be a dark-type GED (Dark GED) is to be explicitly targeted, either by criminals seeking to traffic or profit off such a person, or by those afraid of the dark-type. While they take the bulk, it's not unknown for GEDs of other types to be targeted or persecuted based on outdated beliefs or superstitions. It's said that of GEDs born in a single year, at least half will have been targeted somehow, and 15% of those will have gone missing.