Haven't seen Nikki around in a while...

she's busy moving house I think (from blog stalking her!).
Is the split in the fabric itself or on a seam? If it's in the middle of a panel then your best bet is some iron-on interfacing on the wrong side of the fabric. If it's on a seam, there are some great instructional videos linked to
here (check out the second page for ripped or torn hems).
"Invisible seams" mean different things depending on the context, but in your case probably means a form of hand sewing where you only pick up a couple of threads of the material at a time (working from the wrong side) so you can't see the stitches from the right side - take a look at the bottom of some dress pants for an example.
Seam binding, or bias binding, is a fabric tape which you fold over the seam allowance to finish or reinforce a seam, you can get it from spotlight or any fabric or notions shop.
Hope that made sense!