I have always found it significant that Wittgenstein distinguished between a proposition's sense and its meaning, which is why a sentence can be nonsense (or rather senseless) and be quite meaningful at the same time. An example of such a proposition would be "God is good." Whilst I may not be able to derive a tangible sense from that statement, I can imagine how the statement can be shown to be significant in a form of life, particularly in how and where it is uttered. The opposite is also possible. (NOTE: for the purposes of this entry, I will use the terms sentence and proposition interchangeably.)
To start with, something that makes sense is something that one can imagine clearly or that is perceptible (or simulated) via the senses once the proposition has been decoded and projected. As an aside, a proposition that makes sense does not need to be true. Instead, it must be open to the possibility of being true or false (of being the case or not the case). Consider the sentences of a riveting adventure novel. A world full of characters and events can unfold before the (mind's) eye. And the story can be entertaining, yet maybe not "meaningfully" to all readers.
Consequently, a proposition is meaningful to an individual if it happens to be significant to that individual, which amount to saying, "a statement is meaningful because someone finds it meaningful." That is not quite adequate, so we must go further. I can find a proposition meaningful because it strikes me in such a way, or I know what to do with it, or it plays a part in a practice in my life.
In other words, I sit down and read the proposition and it resonates with me. I find it meaningful. It not only makes sense.
Consider four people who are reading a car magazine article about a new engine modification technique. One person cannot make sense or meaning of the article because the person has little experience with the content. The person can read, but that's not enough here. Another person can make good sense of the article but doesn't draw too much meaning from it, since he has no real need to modify a car at present. The third person finds the article both sensical and meaningful, since he sought out the article since the technique resolves an issue that he must resolve. He reads intently and critically to make sense and to test this understanding in practice. The fourth person is a person who would find the article meaningful if he could make sense of it. In other words, the individual's literacy skills are the limiting factor.
What - then - is the significance about all this chatter? It relates to one learning to read. We must encourage readers to engage with both sense and meaning. We want students to think, "can I make sense of this?" And "now that it makes sense, what can I draw out from it? What has happened and what is significant about this fact?" "How should one interpret this or respond to it?"
We must respect the significance of both steps. It is possible to draw hasty judgements from superficial comprehension as it is possible to get the picture but miss the point.