When reading Derrida it is important to understand that he is primarily a critic of criticism. His goal is usually to critique the way that we interpret and construct meaning. Notably, he quotes Montaigne at the top of his famous essay, "Structure, Sign and Play in the Discourse of the Human Sciences"

"We need to interpret interpretations more than to interpret things."

This notion is very helpful in discussing the ideas of the transcendental signified and the transcendental signifier.

To speak generally about Derrida's critical project, we can say that Derrida works to question presumptions of ethnocentrism and, in his words, the "logocentrism" that is inherent in structuralism. Briefly and broadly stated, the idea that Derrida attacks is one that presumes the existence of a single truth or meaning that is accessed, expressed or referred to in all works of literature and which also, crucially, implies that the center of meaning is located (1) more or less within the scope of human understanding and (2) more or less within the cultural bounds of a single, European culture. 

"Derrida argues that logocentric thinking, which is phonocentric and ethnocentric as well, presupposes universal truths that may be critiqued as cultural constructs or comforting linguistic fictions" (eNotes). 

The idea of the transcendental signified is directly related to the idea that there may be a center of meaning which is somehow indicated, pointed to or approached via works of expression like literature. We might call this center the "ground of meaning" that is used, consciously or not, as a primary reference point without which no meaning could exist.

This presumption that a center must exist (or a central reference point) in order for language to convey metaphysical meaning or "real truth" is exactly what Derrida attacks in his work. To read under the auspices of structuralism, for Derrida, is to construct a false context for meaning.

Assuming that all works of literature relate in some way to the same center of meaning (the "transcendental signified") is to presume that language has a solid foundation in that signified and, therefore, the "book" becomes understood as a universal/transcendental signifier - always approaching the same ground of meaning in order to take on any meaning at all. If there is a center of meaning and if all books are effectively undertaking the same project of indicating that center and if that center is existent somehow within language, one unavoidable conclusion for Derrida is that the culture utilizing such an interpretive scheme is also setting itself up as the arbiter of that center, the purveyor of that literature and the well-spring of that language.

In other words, if one presumes a single answer to the question of meaning and also presumes access to that answer, one is also presuming a power or ownership over meaning itself.  This idea runs against the grain of critical thought in the 1960s as theoretical/critical Marxism began to filter out into feminist theory, post-colonial theory and other critical schools of thought. Like  the critical work of Foucault, Derrida's work seeks to suggest that a theory of meaning which gives authority to a single interpretation becomes a systematic tool to perpetuate views of cultural superiority. 

The terms in question here then can be understood as important conceptual tags that describe the critique Derrida brings in his work against structuralism. 

By "transcendental signified," Derrida meant a concept that is universally true, across cultures, that we can build a philosophy or an intellectual system upon. This might be, for example, masculinity. By "transcendental signifier," he means basically something that enables us to express or understand that concept, like, for example, the phallus. However, Derrida doubted that the transcendental signified existed, in other words, that masculinity, to use my example, could be boiled down to one universal attribute that makes it what it is across cultures. Derrida's work is notoriously difficult to understand, and I have linked to a couple of summaries that might help.

http://www.enotes.com/jacques-derrida-salem/jacques-derrida

http://www.enotes.com/grammatology-salem/grammatology-0265100053

http://www.enotes.com/writing-difference-salem