It is a matter of dispute as to whether Plato ever intended to convey through his Dialogues a "theory of forms" or "theory of Ideas," in which super-sensible forms or ideas are held to be both the ontological foundation of sensible realities and epistemological requirements for our knowing entities in the sense-world. For that, a series of arguments emerge in the Dialogues which have been understood in the Western tradition to offer such a theory, and these arguments remain important elements in the on-going debates between "realists" and "idealists."
In outline, some of the arguments seek to establish:
[A] the difference between a Form (as nonvisual, general [and thus knowable only by the mind] and as perfect) and particular entities (as visual, and thus known by the sense(s), particular, and imperfect);[B] the Form as more real (as it endures and remains the same), over against a particular manifestation or "image" of the Form (in the sensory domain) as less real (as changing and eventually fading into nothingness);
[C] the Form as necessary to knowledge. These arguments include:
I. the difficulty of arriving at the Forms "from the bottom up" (i.e., by beginning with sense experience), since:a) it is hard to see how muddling about in the domain of multiple, different, changing, particular, imperfect entities would lead to a single, unchanging, general or universal, perfect "idea" or Form of something, and
b) it would appear that even to recognize what is before one (as a triangle, a square, as beautiful, etc.), one must already have access to the Form as the standard or paradigm by which an entity in the sense world is "known."
II. the psyche's eros, as the desire for completeness, and as left unsatisfied by the many but imperfect beautiful entities (either on the level of sense or of soul). (This is Diotima's argument in the Symposium, and needs especially careful attention.)
These arguments, moreover, are central to a larger project of Socratic and Platonic (if not Aristotelian) philosophy - namely, to "save philosophy" in the face of several complex dilemmas.
Briefly, the philosophical project, initiated by Thales and the Milesian nature philosophers, began as an effort to provide an account (a logos) of the natural order (physis) -- an account based on human reason (logos) and thus resting on assumptions regarding the intelligibility of the universe to human reason. This project, over a period of less than 200 years, results in a diversity of physical theories -- including evolution (first in Anaximander and then Empedocles) and the spectacularly successful atomic theory of Democritus.
Inspired partly by the apparent successes of the physiologoi ("those who give a logos about physis - nature"), the Sophists began with the serious intent to replicate in the domain of ethics and politics what the earlier philosophers had achieved in the domain of physics. However, their search for a human nature and set of ethical and political values which transcended cultural differences and are thus universal, fueled especially by the relativistic tendency of atomism, concluded with a Sophism which argued first of all for ethical relativism (on the basis of the cultural relativism, already well-documented in Socrates' day).
The rise of Sophism, however, led to especially troubling cultural and political consequences, beginning with the rise of a peculiar sort of anarchy, as the individual quest for complete power (in order to always be able to fully satisfy one's desires), justified by ethical relativism, thus lifts up the ruthless tyrant as the happiest man.
In reaction against this relativism and anarchy, others argued for a return to dogmatic or absolutist religion, for the sake of restoring social order.
In this context, philosophy -- as the rationally-based enterprise of developing an account of both the physical and ethical/political worlds -- is thus faced with an apparently intractable dilemma:
either we take up reason, only to land in Sophism, the pursuit of tyranny, and an accompanying anarchy --or
we abandon reason and return to the social and political stability provided by dogmatic or "absolute" standards imposed by the old religion.
In Plato's Dialogues, Socrates seeks to establish a middle ground between these two poles of the dilemma. The Theory of the Ideas, traditionally understood, is also central here. The Ideas would save philosophy from the epistemological relativism -- one which calls into question the ability of reason to achieve its ambitious goal of providing a coherent account of the order of the universe - and thereby from the ethical relativism of the Sophists. At the same time, such Ideas - as including the Ideas/Forms of justice, beauty, the Good, etc. - are clearly philosophical conceptions, not religious doctrines. Finally, the Ideas - in anticipation of Aristotle's doctrines regarding the mean, etc. - are norms which allow for a variety of interpretations/applications/understandings, not a single "wholesale" understanding. As such, they are key examples of the rationalist pluralism I describe in the materials on "Reason, Revolution, Relativism, and Reactionaries" - especially as they overcome the otherwise apparently intractable dilemma between ethical relativism and absolutism/dogmatism.