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Generally speaking an “allegory” is taken to mean “whenever one speaks of one thing by means of another thing,” yet this is not its proper and specific definition which the Apostle uses in this passage and which Holy Mother Church defines it as. The Gloss gives a helpful definition, Dicitur quod aliquid aliud videtur sonare in verbis et aliud in intellectu significare (something sounds in words and something else signifies in the intellect).
To embark on answering this question, we must first dive into the nature of signification. For, words are certain artificial signs that signifies something existing (whether in the world, i.e., real beings, or in the mind, i.e., being of reason). This signification can be in two modes, immediate, or mediate. Immediately, this is done according to a first order of signification, i.e., the word blue signifies the reality of blue. In this, we can either speak properly, through the “bare signification” of words, or, improperly, through certain metaphors. This “immediate signification” is referred to as the “literal sense” with two species, the proper literal sense and the improper literal sense. Thus, for example, when I speak of my “right hand” I am speaking in the proper literal sense, yet when I am speaking of God’s “right hand” (Ps. 139), I am using the improper literal sense. For, I am only speaking of some analogous likeness found between God and a right hand. This is found in that both can “hold” something, I hold a pen while writing, God “holds” us by his providence.
Second, a word can be a certain sign that signifies something mediately. That is, a word signifies a certain reality through the instrumentality of another mediating sign in a second order of signification, i.e., blue refers to the color blue which is itself symbolic for sadness. This mediate signification can be be done in two modes, first, appropriative, and, second, primarily. The appropriative mode of mediate signification is done when a certain thing is appropriated as a sign for something else, thus, our example of blue for sadness, blue was not created by the author of the poem, rather it was appropriated as a sign for sadness. This is the improper mode of mediate signification in which creatures partake in (for, we are only said to “create” in an improper sense, rather, we refashion and reappropriate creation).
Second, a sign can be created ex nihilo and established in itself as a sign that signifies something else. The later, the proper, primary mode of mediate signification, is the Spiritual sense of Scripture. For, those things therein are established by God not only as things signified by the words, but are themselves investigated with significant meaning and are signs themselves. Thus, lambs were created by God as signs that signify the meekness of the incarnate Lord. Such a seminent is expressed by an ancient author who taught that “water was created in view of Baptism.” Water was not “appropriated” as some “useful sign” for regeneration, but was created and appointed for that purpose of signification (and instrumentality). Why does water wash off stains? Water washes off saints because it was created in view of its purpose in Baptism, washing away the stains of sin. It is a grave and atheistic error to posit that these signs are merely appropriated.
The Spiritual sense of scripture is a genus with three species depending on the terminus ad quem and the terminus a quo of their signification. First, there are those that are Old Testament realities that signify the New Testament, thus it is said to be properly allegorical. Second, there are those that are New Testament realities that signify heavenly realities, thus it is said to be anagogical. Third, there are those things done by those who stand in persona Christi, and, therefore, are to be done by us, as St. Paul establishes when he writes that we ought to “be ye followers of me, even as I also am of Christ.,” thus, the moral sense.
Going back to the improper mode of mediate signification, this is named the “accommodative sense” and is neither purely literal, nor purely spiritual. Such an example in scripture is that of the unity/multiplicity of the body of Christ, where, due to a certain likeness, a certain type of sign is present by analogy. First, we may consider it as internal, i.e., the accommodation is made by scripture itself, second, we may consider it as external, i.e., the accommodation is made by Theologians.
Second, according to the terminus a quo, for, scripture in some places accommodates scripture, and, in other places accommodates natural realities.
Third, according to the mode of analogy. For, analogy can be said in many ways. First, the analogy may be made after the manner of an analogy of attribution, second, after the manner of an analogy of proportionality, either improper or proper.
Thus, to summarize, there can be signification by words (literal) either proper or improper. There can be signification by things, first, appropriative, which can be done by scripture itself (internal) or by theologians (external), accommodating either scripture or natural things, and after the mode of either an analogy of attribution or an analogy of proportionality, which can be either proper or improper. Second, the signification by things can be primary (what is frequently spoken of as the “spiritual sense”) which can be allegorical, anagogical, or moral depending on the termini.