The TL;DR is that it's used by debuggers to set a breakpoint in code.
For example, if you're familiar with gdb, one of the simplest ways to make code stop executing at a particular point in the code is to add a breakpoint there.
Gdb replaces the instruction at the breakpoint with 0xCC, which happens to be the opcode for INT 3 --- generate interrupt 3. When the CPU encounters the instruction, it generates interrupt 3, following which the kernel's interrupt handler sends a signal (SIGTRAP) to the debugger. Thus, the debugger will know it's meant to start a debugging loop there.
Before replacing the instruction with INT 3, the debugger keeps a note of what instruction was at that point in the code. When the CPU encounters INT 3, it hands control to the debugger.
When the debugging operations are done, the debugger replaces the INT 3 with the original instruction and makes the instruction pointer go back one step, thereby ensuring that the original instruction is executed.
The debug version you compile doesn't affect the code; it just stores more information about symbols. The whole shtick about the debugger replacing instructions with INT3 still happens.
You can validate that the code isn't affected yourself by running objdump on two binaries, one compiled with debug symbols and one without. Otherwise if you're lazy (like me 😄):