Posit that throughout your day you interact with innumerable people, but these people as they see themselves in interaction with you, speak and operate in a sort of identification with the "ego" that resides in them. For Lacan, this "ego" (the image we all have of ourselves and that we speak from when interacting with others) is a fiction.
Being a fiction, he doesn't want to make this the target of his focus. It doesn't help him in his endeavor to discover what truly ails or drives a person (a patient, a lover, an enemy etc). The ego isn't ignored however, it's just called the "subject of the statement", an idealized presentation created by the subject of enunciation as a means of reflecting to different others the mirror that enunciative subject unconsciously develops as a coping mechanism for the endless array of social settings and demands this fragile ego tells itself it needs to interact with and survive. The "I", the "ego", the "subject of the statement" is viewed as a signifier and indexical because it allows to understand both it's (the subject's) statements, and ultimately, the subject of the enuciation.
The subject of enunciation is what in Freudian terms would be called the unconscious. It is the same subjects that you encounter in your interactions but the parts that is hidden from their ego. It is more precisely all the agencies that speak through the subject of the statement. Your neighbor sees all of his action and utterances as sovereigns acts that he does in full independence of everyone else. What is revealed through the recording of the subject of enunciation is a an amalgam of agencies (forces in Nietzschean terms) and the neighbor is the agent.
What this means is that truth is always deceptively divided in the individual. There's the truth as the subject of the statement presents it to itself and to Others, and there is the truth that is only uncovered through the analysis of the statement of the encunciation.
E.g. he states in Seminar XI of the Ecrits:
[The] division between the statement and the enunciation means that, in effect, from the I am lying which is at the level of the chain of the statement – the am lying is a signifier, forming part, in the Other, of the treasury of vocabulary in which the I, determined retroactively, becomes a signification, engendered at the level of the statement, of what it produces at the level of the enunciation – what results is an I am deceiving you. The I am deceiving you arises from the point at which the analyst awaits the subject, and sends back to him, according to the formula, his own message in its true signification, that is to say, in an inverted form. He says to him – in this I am deceiving you, what you are sending as message is what I express to you, and in doing so you are telling me the truth (S XI, 139-40).
While the statement of the subject can be easily indexed according to Lacan and is fairly predictable like any other object, the subject of the enunciation is by nature multiplicitous.