Suica is a pre-paid IC card issued by JR East to travel around Tokyo and also other major cities in Japan. It also can be used for shopping at registered shops including major convenience stores, shopping malls AEON, electronic stores BIC Camera and Yodobashi Cameras and many more.
Pasmo is also a prepaid IC card issued by the Tokyo Metro which can be used to travel on the Metro, JR and other trains. Just touch the card on the card reader when you start and end your journey.
Both cards can be purchased at stations in Tokyo. In other major cities (Osaka, Fukuoka, Nagoya Sapporo) also offer similar IC cards such as ICOCA, Kitaka, Sugoka, Manaca, Nimoca etc. which can be used throughout Japan.