1) At the bottom of the bank screen you will see 2 new buttons marked 'insert' and 'swap'.
'Swap' mode is the mode you are used to, whereby when an item is dragged to a new slot it swaps places with the item already there. This works exactly the same way as before.
'Insert' mode is a new option. In this mode dragging an item to a new position causes it to be inserted at that point, and everything else is moved up one space to make room. This is useful for instance if you get a new rune, and you want to place it next to your existing runes without having to manually move everything else.
2) It is now easier to move items a long way across your bank. Now if you drag an item to the top or bottom of the bank window, the window will automatically scroll up or down for you. This makes it much easier to move items several rows at a time. (note: this particular feature has actually been online for about a week now, but wasn't mentioned before so is here for completeness.)