Bitcoin is a type of cryptocurrency: Balances are kept using public and private "keys," which are long strings of numbers and letters linked through the mathematical encryption algorithm that was used to create them. The public key (comparable to a bank account number) serves as the address which is published to the world and to which others may send bitcoins. The private key (comparable to an ATM PIN) is meant to be a guarded secret and only used to authorize Bitcoin transmissions.
Style notes: According to the official Bitcoin Foundation, the word "Bitcoin" is capitalized in the context of referring to the entity or concept, whereas "bitcoin" is written in the lower case when referring to a quantity of the currency (e.g. "I traded 20 bitcoin") or the units themselves. The plural form can be either "bitcoin" or "bitcoins."