This is an extremely important distinction and one which is difficult to gain. Spinoza is discussing a framework of two accessible attributes: thinking and extending. These attributes are perspectival and reflect independent views or aspects of the same reality. However, human finite capacities and mental tendencies cause them to be seen as causing one another rather than simultaneously reflecting the same underlying reality.
As a result, ideas tend to be inadequate because they are either poorly constructed (such as illogical) or because they are derivatively rooted in perceptions of the object rather than fundamentally rooted in a causal chain of adequate ideas of underlying reality. Adequate ideas are concepts of the active mind (II.D3) because they connect with expressiveness, whereas inadequate ideas (even though scientifically tested of objects) cause a passive mind as inert reflections of an expressive mode within another attribute (namely that of extending). The result is a loss of power for the mind (active to passive) as its ideas are grounded in a mirroring of extending rather than rooted in the reality of substance. This difficult distinction is important to the achievement of blessedness as that state is one which reflects power. Essentially for Spinoza, unhappiness is a thinking problem based on inadequate ideas.Per ideam adæquatam intelligo ideam quæ quatenus in se sine relatione ad objectum consideratur, omnes veræ ideæ proprietates sive denominationes intrinsecas habet.
Explicatio: Dico intrinsecas ut illam secludam quæ extrinseca est nempe convenientiam ideæ cum suo ideato.
Translated as,
By adequate idea, I understand an idea which insofar as it [the idea] is considered in itself and without relation to an object, has all of the properties and intrinsic denominations of a true idea.
Explanation: I say intrinsic [denominations] so that I might shut off the idea's conformity, which of course is [an] extrinsic [denomination], with that of which it is the idea.
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