A simple answer would be to say that the Soul historically is whatever part of a person there might be that is not their body. Yet why should we think that Souls should be taken to exist, and whether Souls could be Christian or moral or anything else?
Michel Foucault, in his Discipline and Punish (1977), presents a genealogical analysis of his society's view on behavioural deviance and its responses to it. Early on in the work, Foucault presents before us an interpretation of his work which I find compelling:
This book is intended as a correlative history of the modern soul and of a new power to judge; a genealogoy of the present scientifico-legal complex from which the power to punish derives its bases, justifications and rules, from which it extends its effects and by which it masks its exorbitant singularity. (p23, Ch 1, "The Body of the Condemned")
Foucault argues that the move from torture and death to imprisonment and reform plays into the technologies of power that serve to influence the modern notion of the self. That is, that what is involved in present-day societal functions of discipline, the law and punishment is machinery designed to shape and influence your behaviour, in ways more subtle and influential than threats of harm, in order to make people en masse more ordered and less violent and chaotic.
For Foucault, then, this is exactly the modern soul - something that has been specifically created, through the institutions and disciplinary techniques applied to you in childhood and continue to be at work in "civilized" society, to serve as your moral centre in the absence of direct individual coercion. Other theorists have called this "Conscience", the "Id" and various other labels. Typically then, debates about the "soul" are of less broad interest than debates about the mind, which certainly invites a lot of discussion: See for instance the introductory SEP article on Dualism and the Mind Body Problem.
The Christian soul can be analysed in very similar terms, though they would be very hesitant to give a genealogical analysis. Your soul is something given to you by God, it is that in virtue of which you are what you are in the scheme of God's intention for the world, it is what is at stake in matters of adherence to religious doctrine and practice, and it is the source of your existence beyond your physical presence on the earth, for which you will experience either reward or punishment in the eyes of God. For a Christian, your soul is you, but specifically you within the context of a Christian perspective.
Foucault might note that such a perspective is no accident, but is yours by virtue of various disciplinary and manipulative functions brought into practice upon you to write you into a docile Christian. Where Christians differ from Foucault of course is that they argue that your soul is something that is present within you certainly from the moment you are born to the moment you die (and beyond), and that is the creation of the Christian God regardless of whether or not you actually subscribe to the Christian faith or live in a world in which it exists. This might be read as a kind of claim for totalizing power over the right to dictate behaviour, which Christians will hold is God's (or from the analyst's perspective, Christianity's) by virtue of his power and benevolent will.
It is difficult to challenge this position philosophically, because a primary issue as to the existence of their God or their souls is not a metaphysical or scientific one but rather a political one - specifically, what, exactly, does this particular series of behavioural manipulations through Churches, Christian doctrines about the family, about conduct in business and community engagement, about personal health and well-being and more, actually look like? How much of a difference have they made in the lives of others, what comfort and support have they offered the world, how is the world better for their being here than not? Maybe it really does work out for the best. I am firmly sceptical (and am regularly reassured as to that scepticism), but that's what it comes down to.
The way to react to a Christian who relies upon their soul to justify their actions is just to look at their actions and challenge them independently if they are in need of challenging. That is their concept of "soul" at its most vulnerable.