The irony of reality
Although we believe in reality a certain way scientifically, Russell notices that most people never actually apply that scientific, technical knowledge to their actual understanding of reality. His example is that a table is actually mostly vacuum with a hysterically small amount of actual matter, and yet to the human eye is seems perfectly obvious that it is "solid," but solid in a less technical sense. Ironically we aren't even perceiving what we understand scientifically to be true.
The irony of metaphysical philosophy
Metaphysical reality is technically absurd, because reality seems so perfectly evident. There are questions that can break the illusion of reality's self-explanatory feel. Asking the questions of metaphysical reality is like breaking the fourth wall. Irony is literally part of the metaphysical design of the human life, suggests Russell.
The irony of perception
Trying to analyze the nature of human experience leads Russell to this irony, because humans attempting to understand their perception of reality only have their perception to go on, so immediately, the effort begs the question. Russell's ideas try to push past animal participation in reality, trying to interpret perception itself somehow.
The irony of philosophical progress
One would suspect that after having done philosophy for basically the entire history of humankind, that more progress would have been made on the essential questions about human nature, about this reality that Russell encourages his reader not to just take for granted. But, philosophy is a human endeavor, and Russell realizes that although the full weight of ethos leads people to believe things they can't prove, he himself can see a new kind of philosophy where no assumptions are made. It's ironic that his assumptions about philosophy led him to be severely disappointed in the lack of human curiosity.
The irony of description
To describe one's experience of reality is a fundamentally ironic endeavor, because it presupposes that although we all belong in the same shared domain of reality (the earth), we are so unique in perception that reality might literally mean different things to different folks. By describing reality, Russell feels that a person could wisely avoid trying to explain its causes. He wants to answer as many philosophical problems as possible without resorting to any authority other than pure intuition.
