My question is - what does placing the wire XY perpendicular to the plane of paper mean?
It means you poke the wire through the paper. If you were to shake some iron filings on to the paper they'd line up along the magnetic field lines like little compass needles. The magnetic field lines can be drawn like this:
By the way, despite what you might be told by people who can't answer your questions, there are people who understand magnetism and how it works. Don't listen to people who tell you physics can't supply the answers. It can. That's why we do physics. We do physics to understand the world, not to make predictions. Don't forget that Maxwell wrote On Physical Lines of Force. The force is real, and so are those iron filings and the pretty patterns:
Whilst there are no "lines of force" per se in the space around the wire, they do map out something real - a magnetic field. Electromagnetic field interactions result in linear and rotational forces. A uniform magnetic field is a place where the linear forces cancel, but the rotational forces do not. Hence when you throw an electron through the middle of a solenoid, it follows a helical path. Note though that a typical magnetic field is not uniform, and so we see linear forces too. Hence two wires like the above attract one another. But if you reverse the current in one of the wires, they repel.