HD is short for Hierarchical Deterministic.
Typically, bitcoin wallets generate each new bitcoin address from a unique random number, requiring you to make a new separate backup each time you create a new address. To avoid losses from lack of backups, such wallets tend to use a single bitcoin address for all transactions.
HD wallets instead use a «master seed» (a number based on the 12 random words in Mycelium's case), to derive all future bitcoin addresses sequentially, with each new address created by appending a counter to the end of the seed. In this way, all the bitcoin addresses created by such wallets are «hierarchically determined» from a single seed, only need to be backed up once, and can be fully restored at any time in the future just from the backup of that single master seed. When using a single address wallet, all your transactions will be associated with a single address, and because all bitcoin transactions are public, anyone can see what addresses you are sending funds to and how much money you have.
The Backup gives the wallet a "starting point" (a secret) from there it is able to reproduce everything else it needs as it always does it the same way. This way you also only need to back it up once and not every time you add an address to your wallet.
HD wallets greatly improve your privacy by being able to generate new addresses whenever you send and receive funds, making your transaction activity and total balance very hard to track.