Supra-aural headphones or on-ear headphones have pads that press against the ears, rather than around them. They were commonly bundled with personal stereos during the 1980s. This type of headphone generally tends to be smaller and lighter than circumaural headphones, resulting in less attenuation of outside noise. Supra-aural headphones can also lead to discomfort due to the pressure on the ear as compared to circumaural headphones that sit around the ear. Comfort may vary due to the earcup material.
Cable dressing and length: Most stereo headphones have just one cable, usually attached to the left earpiece (sometimes called single-sided cabling). Some models -- and all earbuds -- use a Y-cable that connects to both earpieces (double-sided). The actual cable plug, meanwhile, is usually one of two designs: a straight I-plug or an angled L-plug; the latter may be useful if your portable player has a side- or bottom-mounted headphone jack.
If you just want to block out sound without active noise cancellation, good over-ear headphones will naturally do that to some extent. This is called noise isolation, and it simply works from the earcups forming a good seal over your ears to prevent outside noise from getting in. It's not as effective, but it's less expensive than active noise cancellation and doesn't require power.