These abbreviations stand for the hashing power that your miner is generating. MH/s stands for megahash per second and GH/s stands for gigahash per second. There is a direct correlation between how fast your miner works and how profitable it will be.
Use http://www.bitcoinx.com/profit/ to calculate the profitability of mining under varying circumstances, to include difficulty increases, power consumption, and average hashrate, for example.
The term "hashing" means how quickly your hardware is processing data from the Blockchain and solving the complex mathematical equations that are required to earn bitcoins.
A mining pool is a group of miners who have shared their hashing resources to solve blocks together and the rewards are then distributed amongst the members.
A Graphics Processing Unit powers most computer video cards and can be used to mine Bitcoins.
A share is merely an accounting method to keep the miners honest and fairly divide any rewards earned by the pool.
An Application-Specific Integrated Circuit is a special chip designed specifically for mining Bitcoin and is much more energy-efficient and faster than GPU or FPGA mining.
A Field-Progammable Gate Array was already an established hardware product that can be used for different purposes, but in this case the technology was repurposed for mining Bitcoin.