The path is a long, dark hallway that travels under Saffron City. Despite the cave-like lighting of the path, there is no threat of being attacked by wild Pokémon. Occasionally, by using an Itemfinder, items that Trainers have dropped along the path can be found and retrieved.
The only difference across all four generations was the removal of the Underground Path as a playable area in GenerationsII and IV. The reason is explained in a note from the Celadon Police left on the signpost to the Underground Path in Route 7.
There is a notice!
...Uncouth Trainers have been holding
battles in the Underground Path.
Because of rising complaints by local
residents, the Underground Path has
been sealed indefinitely.
Signed, the Celadon Police
There is no equivalent notice on Route 8's entrance, though the signpost there does imply that it used to have one. It is possible that the Bikers fought there are responsible since one of them comments about the police closing it down.