Did the Buddha ever define what he meant by "self"? Added: I am asking this because I am not sure if anything I observe would be considered "self" according to the Buddha. I don't have this problem with craving or suffering because I can observe/experience craving and suffering and it seems quite clear that they can be and are defined as such.  

It seems to me I am unable to determine whether there is, isn't, what is or what isn't "self" because I don't know what aspect/s of reality the word "self" is defined as corresponding to. 

I am wondering if it is possible to describe what aspect/s of reality the word "self" is defined as corresponding to.  

It looks like the Buddha  may have defined the aggregates as "not-self" so if there is a "self" (What is a "self"?) then according to the Buddha it's definitely not the aggregates. In my opinion this cannot simply be a "view for practicality" because then the Buddha would be a liar in that case.
"Self" is this highly childish, simplified, vague, unexamined idea in your mind: "This is me". It's not a concrete thing, it's an overall thing, it's a blob: "I am such, overall". It's an overgeneralization and an oversimplification.

It exists exactly because it's unexamined, and because it exists it attracts all kinds of funny ideas. For example, you may assume that "I am a good person" or "a bad person" or "a horrible person", or smart, or stupid, or ugly and so on. Self is like a Christmas tree on which we keep hanging all these ideas - but if you look carefully, there is no tree. It's all made of the decorations, or ideas - hanging on each other!

That is the point!

We acquire an opinion about politics, or some kind of judgement about the world and we add it to the tree. Then we identify with it so completely that this opinion becomes our second nature. It is natural to us to think that (put some popular controversy here). So once there is self, once there is this Christmas tree of ideas we have internalized and identified with - about ourselves, the world, and everything in between - we begin to see things a certain way, a certain reality arises in our mind.

But this reality is not THE reality. This reality is a projection of the Christmas tree! It's a shadow or a reflection of our conglomerate of ideas.

So when Buddhism talks about no-self in practice it first and foremost means getting rid of this deep fundamental assumption that reality we see is actual reality, and our idea of self is actually a truthful representation of how things are.

To this goal we are instructed to examine our immediate experience (thoughts, emotions, interpretations, perceptions etc.) until we see how the Christmas tree is made.

Then of course we see that what we thought were our "choices" and "actions" were actually knee-jerk reactions and impulses coming from the Christmas tree. We realize that all speak of free-will is nonsense when we are in fact driven by our ideas like sheep, and freedom is only possible when we un-identify from all that and learn to be nothing (yeah, like Arya Stark).

When we are nothing, we are free, because there is nothing one can point to and say this is us. When this happens, the notions of death etc. are no longer applicable - because the object it was supposed to apply to only exists in the unenlightened mind, but we don't have to hold on to that.

This, generally, is the overall context in which these conversations about No-Self happen in (Mahayana) Buddhism. At least, this is how it is from my perspective, but mine is not final of course. For example in Theravada, the no-self talk is primarily ordered around Five Aggregates, which from Mahayana perspective is nothing but a didactic device to provide an alternative functional interpretation of Everything that would not involve a notion of single agent or single observer. So Theravada is slightly more concerned with the low-level phenomenology of observation and action while Mahayana is more concerned about the higher-level (social and psychological) manifestations of the same illusion of a single solid entity.

Anyway, what's important to understand for a beginner is that "self" is this unexamined blob, which seems like you until you start analyzing it. I am this, I am such, I like this, I hate this, This is right, This is wrong - all this stuff bundled together into one "This is who I am and this is why I do what I do" - is the self.