From David Adger (2003), Core Syntax - A Minimalist Approach, p. 19:
[Syntactic] features that have an effect on semantic interpretation [...] are called interpretable features.
Person, number and gender are examples of interpretable features in English:
(13) The child wails
(14) The children wail
The plural feature clearly has an effect not just on the morphology of the word, but also on its meaning: in this case it affects whether we are talking about one child or more than one; one man or more than one, and so on.
On the other hand, case is an example of a feature which is uninterpretable in English:
(68) We all thought him to be unhappy
(69) We all thought he was unhappy
In the English cases the semantic role of the pronoun whose case is being varied does not seem to change. In both cases, whoever the pronoun refers to is being unhappy. We will see in a later chapter that the semantic role of a word depends on other aspects of its syntax than case, and we shall assume, for the present, that the function of case is purely syntactic, and that it is an uninterpretable feature.
Note that which features are interpretable is language-specific though; there are languages where syntactic gender is not or not always semantically interpretable, and others where case is directly accessible to semantic interpretation rules and not only required for syntactic reasons.
Adger's theory assumes that all uninterpretable features eventually have to be eliminated (by the syntactic operation of feature checking) from the syntactic structure before it can undergo interpretation by semantic interface rules, because semantic rules can only make sense of interpretable features.
So the distinction is whether features that are present morphosyntactically will also appear on the level of LF.
PF plays no direct role here since some morphosyntactic features may be realized due to the phonetic presence or absence of certain endings, e.g. singular number in English is usually indicated by there not being an "-s".
I don't have the Bailyin book and don't know much about Russian, but I understand the cited paragraph as meaning that there are some grammatical restrictions on when a word can be in instrumentative case, namely only when there are no features like number, gender etc. in the structure that are available to semantic interpretation, and even then the word or phrase will not have the semantic status as the core action or attribution of the sentence, presumably because being the semantically primary predicate would require the presence of something interpretable in it.