A "game term" in refers to a term used in the rules-engine part of the game, and takes on specific meaning as part of the resolution of rules. This as opposed to the "regular English" meaning of the word, which is just what you get in a dictionary and is used in the fiction part of the game.
Sometimes the two mean completely different things. This usually doesn't cause any issues, but for example 'Move' means very different things in plain English (where it refers to someone changing their location) and a Powered by the Apocalypse game (where it defines an in-fiction trigger and the consequences that happen when triggered).
In the above case, "Move" as a game term is very different from "Move" as an English term, and asking about Apocalypse World "Which move lets me escape a fight?" cannot be answered just by looking in a dictionary.
However often the "game term" and "dictionary term" are a lot closer and it can get confusing. For example, Dungeons and Dragons 5e has a game term called 'Proficiency', which has a meaning pretty close to the normal English word (being good at something)
This can sometimes create confusing situations. Imagine a D&D character who has very high Strength, but no formal training with swords. The player might describe the character as "proficient with a blade" simply because they get a comparable attack bonus to a trained soldier, and that wouldn't be wrong based on the english meaning of the word. But if the DM then asks "But are you actually Proficient with that weapon?" the answer switches from normal English ("I'm proficient with this weapon; I can hit as easily as a soldier can") to a game term answer ("No, I'm not actually Proficient with my sword.")
Whenever someone explicitly refers to "what does this mean as a game term" it means the question is probably about this difference. Due to the complexity of roleplaying games and the desire to keep books reasonable, sometimes rulebooks will mix up game terms and normal language.
This might lead to question like "what's the difference between what this word normally means, and what it means in this game context?"
An example might be parsing a line like:
"Requires: Strength 16+, Proficiency with a Longsword, being a Knight"
The first one is almost certainly a game term, the second one probably is (and clearly will be read as such in any game that has previously explained that Proficiency is a core rule to the system) but the third one might confuse people.
Is Knight some kind of class you can take levels in? Does it mean you need to be an official member of an order? Are there rules for that? Or is it just a fictional requirement and does your character need to consider themselves a Knight? As soon as two players disagree, you're likely to end up with a question like "Is Knight a game term?", because people want to know if "Being a Knight" is defined as a game rule somewhere, or whether it's just a fictional requirement.