A idea of what Peirce means by an Interpretant and the part it plays in a triadic sign relation is given by the following passage.

It is clearly indispensable to start with an accurate and broad analysis of the nature of a Sign.  I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former.  My insertion of “upon a person” is a sop to Cerberus, because I despair of making my own broader conception understood.  (Peirce 1908, Selected Writings, p. 404).

According to his custom of clarifying ideas in terms of their effects, Peirce tells us what a sign is in terms of what it does, the effect it brings to bear on a “person”.  That effect he calls the interpretant of the sign.  And what of that person?  Peirce finesses that question for the moment, resorting to a “Sop to Cerberus”, in other words, a rhetorical gambit used to side‑step a persistent difficulty of exposition.  In doing so, Peirce invokes the hypostatic abstraction of a “person” who conducts the movement of signs and embodies the ongoing process of semiosis.

Reference

• Peirce, C.S. (1908), “Letters to Lady Welby”, Chapter 24, pp. 380–432 in Charles S. Peirce : Selected Writings (Values in a Universe of Chance), Edited with Introduction and Notes by Philip P. Wiener, Dover Publications, New York, NY, 1966.

Resources

• Hypostatic Abstraction
• Survey of Semiotics, Semiosis, Sign Relations

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