Well, maybe the first poster means the Jersey City end of the Skyway. There are at least 4 possibilities -- looking at a satellite photo like at maps.google.com will help sort it out.
Right after crossing into Jersey City, down below on your left, not quite parallel to the Skyway but angling toward it are the freight line coming from Meadows Yard (South Kearny?) that the previous poster mentioned, and PATH tracks running right next to each other. Both were once part of the Pennsylvania RR, originally freight and passengers (to Jersey City /Exchange Place)) This line then goes under the Skyway -- you are at the spot when the Skyway itself is supported by a metal trestle you can see on both sides of the Skyway. You then might be able to see the line on your right heading towards Exchange Place. SOmeone else will know when the last regular passenger trains ran (besides the PATH predecessor Hudson Tubes).
Right after this another frieight line branches off the first one (at Marion Junction as mentioned before.) This line then heads north, going back under the Skyway more or less at right angles to it, and the Skyway is supported by another trestle at this spot. This freight branch is called the Northern Connection I think, linking up a few miles north with the "River line" (which runs north along the Hudson river in NY state further north). Or maybe all of this section is called the River Line now. (This section was originally part of the Erie RR, and maybe shared by the New York Susquehanna and Western, for freight.)
Third, as the Skyway then approaches the ground, just before Routes 1/9 turns left to head north as Tonnele Ave, on the right is a 3 or 4-track passenger line, with electric wires above each track roughly parallel to 1/9. It crosses over the previous "Northern" line and then under Tonnele Ave at right angles, and then goes into a tunnel into the Palisades beween Tonnelle Ave and JFK Blvd. (Actually, coming from the east, just out of the tunnel, it splits just before the Northern Connection line and there is a bridge for each branch over the Northern. THis might be the area you mean since you say "after the Skyway". This is the NJ Transit line to HOboken, originaly part of the Delaware, Lackawanna and Western and later the Erie Lackawanna after the Erie-DLW merger.
Fourth, branching off the Northern, coming from the north, and then heading southeast, is another freight line on your left, single track. It might be hard to see since it is down low. It goes under Tonnelle Ave north of the DLW line, and then under the DLW line, and then into its own tunnel into the palisades. It used to be an Erie line for passengers (to Pavonia Station) and freight.
All but the NJ transit line are now Conrail and active.