Question

the poor man's material is ironically proving to be highly expensive.explain?

Answer 1

This sentence explains that the poor man's thing or material is very cheap.

Answer 2

In our day to day conversations we often use humour in our speech.Irony is a way of speech humour where we say the exactly opposite thing to build up some humour about a specific subject or circumstances.

Similarly,in the the speaker ironically want to say that the poor man's material is very cheap.That's why he is saying completely opposite that the material is "expensive",to build up the humor about that material's price value.