An IRQ conflict is a particular problem that occurs when two pieces of hardware within a PC try to use the same IRQ at the same time. This can cause all sorts of strange behavior and is uniformly a Bad Thing. Fixing an IRQ Conflict can involve spending hours experimenting by fiddling around with jumpers.
This is one of the reasons the original PC architecture sucks. Modern PC users are less likely to experience IRQ conflicts since most PC hardware now supports up to 16 IRQs rather than 8, dynamically allocating IRQs, and other niceties like Plug and Play BIOSes and the PS/2 mouse.