A prolapsed (slipped) disc is when the squishy innards of the disc (nucleus pulposus) bulge out past the stiffer wall of the disc (annulus fibrosis). The problem is that sometimes when this happens, the bulge can impinge the spinal cord or the spinal nerve root. This could result in an anterior cord syndrome (remember this doodle) or it could just knock out the nerve root, resulting in a specific radiculopathy (check out this doodle for where to check for numbness and weakness).
The tricky thing to remember is that though, for example, the L3 root exits at L3, if the L3,4 disc herniates, it doesn’t hit the L3 root but the L4.
Slipped L3,4 disc = L4 nerve injury
The disc hits the nerve after it has branched off the spinal cord, but before it has exited the vertebral canal.