At its most basic, Bitcoin is a collection technologies and concepts that is in use as a digital currency. The units of currency are known as Bitcoin, with a smaller denominations known as a Satoshi. A single Satoshi is 1/100,000,000 of a Bitcoin and with the value of Bitcoin growing, is increasingly how people transfer Bitcoin.
You can do almost anything that you can do with normal currency with Bitcoin. Bitcoin is the financial equivalent of the internet in that it allows you to send or receive Bitcoin from anyone, anywhere in the world. You can also buy good and pay for services using Bitcoin. There are also other digital currencies which you can buy from Exchanges that trade using Bitcoin.
Bitcoin operates in a de-centralized peer-to-peer system so there is no single point of failure. The currency creation is through a process called mining, where people use computing resources to solve a mathematical problem and validate transactions at the same time. The miners reward is more Bitcoin.
The protocol limits the creation of Bitcoin to a total of 21,000,000. Also, the creation of Bitcoin is halved every four years, which means that all Bitcoin mining will cease in the year 2140. The diminishing rate of creation means the currency is deflationary.
The miners validate a Bitcoin on average every 10 minutes. The Bitcoin algorithm adjusts the difficulty of the algorithm so that the difficulty increases as more miners (and computing power) come on board. Because there are so many people mining Bitcoin, the rewards are very small for those without massive computing power.