Mednafen PSX requires a .cue file to be able to load a .bin/.iso image. If you don't have one, you can create one in a text editor (eg. Wipeout.cue) and include the following lines and then save it:
FILE "Wipeout.bin" BINARY
TRACK 01 MODE2/2352
INDEX 01 00:00:00
Just replace Wipeout.bin in quotation marks with the exact file name of the .bin/.iso file of the game image (eg. FILE "MetalGearSolid.bin" BINARY). Make sure the file name is correct and includes any spaces as this is what points Mednafen to your .bin/.iso.
After you've done that, your game directory should have a Wipeout.bin and a corresponding Wipeout.cue file. When you open up Retroarch, select the Mednafen PSX core, select Load Content and then select the Wipeout.cue file and it should work correctly for you.
Edit: If you want to keep your .cue file in a different location to your .bin file as richisawesome has suggested earlier, you will need to include a full path to your ISO/BIN file in the quotation marks (eg. FILE "D:\GAMES\PSXISO\MetalGearSolid.bin" BINARY)
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Extra edit:
^ That will work with most games if you're stuck without a .cue file but keep in mind that some PSX games with CD audio tracks will need a full .cue file that includes audio track references otherwise the music won't play (the Wipeout games are a good example). Refer to a tutorial for your CD Image creating software if you need to re-rip your PS1 games that have CD based audio tracks, so it will automatically generate the .cue file for you.
A .cue file with audio track references will look like the following when opened in a text editor:
FILE "Wipeout 3 Special Edition (E).BIN" BINARY
TRACK 01 MODE2/2352
INDEX 01 00:00:00
TRACK 02 AUDIO
PREGAP 00:02:00
INDEX 01 08:56:47
TRACK 03 AUDIO
INDEX 01 13:03:05
This is from the wiki and might explain it better:
For most systems, Mednafen only needs the rom file; but to load PS1 games, Mednafen requires CUE sheets to know where the music data is. Ensure that the CUE sheet is properly set up in order for the game to run. See the Cue sheet (.cue) page for more info.
For additional info