The cable that comes from the battery terminal.

If you see sparks it is showing you the location of the bad connection. You got WAY luckier than us. We have to do voltage drop tests to determine the location of the bad connection. You must either clean / repair / tighten the bad connection, or if it's due to a frayed cable, you replace it. The red positive one may be called the battery cable or starter cable. The black negative one can also be called a battery cable, but more commonly the ground cable. If you need to replace one notice they each will have a second smaller wire that attaches to the body or the under-hood fuse box. The replacement cable must have those too. Unless your vehicle uses a specialty cable you can find replacements at hardware stores, farm and home supply stores, or auto parts stores. You'll find some special cables at auto parts stores too and they can look up the right one by application, but for the really odd ones you'll have to order it through the dealer.