There are several points where you will likely encounter fees in the Bitcoin network.
It is free to receive bitcoin but sending usually incurs a fee to ensure timely inclusion of the transaction into the block chain. This is because Bitcoin relies on people all over the world storing the ever-increasing block chain which consumes valuable resources such as network bandwidth and disk storage space. The Bitcoin network is also limited on the number of transactions it can place into a block and as such miners tend to prioritise transactions based on their profitability.
If a transaction provides a fee to the miners then it is very likely to be included in the next block, if not then it may take several hours for a miner to add it. Since most people want their transactions to go through quickly it is common to add a small fee of a few thousand satoshi.
Transaction fees are calculated based on the size of transaction in bytes in terms of storage rather than the value. The rules are a little complicated, but MultiBit HD will work out the appropriate minimum value to ensure timely inclusion of your transaction into the next block where possible.
If you regularly receive lots of very small amounts of bitcoin then you will likely incur larger fees since it will take the inclusion of many small inputs to create a sufficiently large output and these take up storage space. If possible you should try to avoid "dust" amounts which tend to be under $1 in value.
The Fees panel provides a slider so that you can adjust your default fee setting to better match your day to day use. The default value provides a good starting position so that it is likely that your transaction will get into the next block, as of Summer 2015
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