I keep hearing that phrase almost daily without exactly knowing what it means, but only a guess I have made up from the context of the conversation.
What does it exactly mean, and when/where do I use it (without mistakes) myself?
It means : in the context of/as part of/within the scope of.
For example :
Dans le cadre de notre projet d'implantation en Chine, nous avons décidé d'accélérer la production des modèles X
could be translated
In the context of our Chinese expansion project, we decided to accelerate the production of X models
I think it should be "dans le cadre". It means "in the context" or "as part of".
"Dans le cadre des opérations" => "In the context of operations"
Cadre might be feminine nowadays when referring to a female manager/officer/executive (e.g. une cadre supérieure) but preceded by dans, it is an obvious grammar mistake (See TLFi B.-3.), cadre means "frame" here and dans le cadre, "within the limits/context".
Surprisingly, it is not that rare and I found it in a official French writing: