Most of the units of Bitcoin are derived from the fractional prefixes from the SI (International System of Units or Système International d'Unités) units.
The first unit is a Bitcoin, which can be split up to 8 decimal places. Therefore, the smallest unit of a Bitcoin is 0.00000001 BTC, also known as a satoshi (after the founder(s) of Bitcoin). You can fit 100 million of those into one BTC! Here is what you can derive from this:
The Main Units
1 BTC/XBT = 1 bitcoin OR 100,000,000 satoshis
1 mBTC (millibit) = 0.001 bitcoin OR 100,000 satoshis
1 μBTC (microbitcoin) = 0.000001 bitcoin OR 100 satoshis
1 satoshi = 0.00000001 bitcoin OR a 1/100,000,000th of a bitcoin
The Less Common Units
1 bitcent (or cBTC): 0.01 BTC OR 1,000,000 satoshis.
1 bit: 1 μBTC OR 100 satoshis
Those are the units you will normally hear. There are more, but they are not usually used. I hope this will be helpful to some newbies!