It's important to note that the term Parallel ATA used to simply be called ATA. ATA was retroactively renamed to Parallel ATA when the newer Serial ATA (SATA) standard came into being.
PATA cables are long, flat cables with 40-pin connectors (in a 20x2 matrix) on either side of the cable. One end plugs into a port on the motherboard, usually labeled IDE, and the other into the back of a storage device like a hard drive.
Some PATA cables have an additional connector midway through the cable for connecting yet another storage device.
PATA cables come in 40-wire or 80-wire designs. Most modern storage devices require the use of the more capable 80-wire PATA cable to meet certain speed requirements. Both types of PATA cables have 40-pins and look nearly identical so telling them apart can be difficult. Usually though, the connectors on an 80-wire PATA cable will be black, gray and blue while the connectors on a 40-wire cable will only be black.
Note: Even though PATA and SATA are both IDE standards, PATA (formally ATA) cables and connectors are often referred to simply as IDE cables and connectors. It's not a correct usage but it's very popular nonetheless.