As the terms imply, "ordinary speech" is the everyday language that you or I might use as we go about our daily lives. "Elevated language" sounds poetic because it uses literary devices such as metaphor, simile, or allusion. It is not the way we speak in normal life. We need to keep in mind, however, that ordinary speech from almost one hundred years ago might sound slightly different from the way we talk today.
One example of a juxtaposition of ordinary and elevated speech is as follows:
Let us go then, you and I
Any of us could say something similar when it is time to leave for a party. However, this ordinary language is followed by a simile (a comparison using like or as) that none of us would probably ever use in real life. It is elevated diction
When the evening is spread out against the sky
Like a patient etherized upon a table
A second example is the following:
And indeed there will be time
For the yellow smoke that slides along the street,
Rubbing its back upon the window-panes
Again the first line is ordinary language, even if most of us wouldn't say "indeed" in the U.S. in the 21st century. However, the second two lines are poetic, part of an extended metaphor comparing the fog and smoke of the streets to a cat.
Finally, we come to this:
[I] Have known the evenings, mornings, afternoons [of going to parties],
I have measured out my life with coffee spoons
The first line is (more or less) ordinary language--we could imagine saying it to a friend; the second line is a metaphor for wasting one's life over coffee and chat at parties. Unless we know this poem, the second line is not the kind of statement we make in everyday speech. If we do use, it we are being poetic, because we are alluding or referring to this poem!
The language shows Prufrock going back and forth between his everyday world of the here and now and the world of the imagination: he is caught uneasily between the two.