The word itself is derives from traditional Japanese language and aesthetic. It is nearly untranslatable as it describes a feeling which no one has been capable of putting into words. It's closest descriptors are said to be “elegance”, ”grace”, “intimation”, “composure”, “equilibrium”, “serenity”, and “quietism”.
Yugen can be experienced, but not described as this or that. Think for example of trying to describe what exactly love is to someone, you're capable of labeling physical feelings or changes that it might give you, but you can't pinpoint what exactly it is, which is part of the beauty of it. Yugen is similar in this respect, it is in some places 'defined' as: "An awareness of the universe that triggers emotional responses too deep and mysterious for words."