The Bin is a storage block which can hold 4096 of a single item. It will retain its inventory when broken.
A Bin won't be broken by shift-clicking with a wrench as most Mekanism blocks will. It's possible this is a bug.
To store something in a Bin right-click any side while holding an item or stack. This will store what's in your hand. Double right-click to put the complete amount of an item in your inventory to the bin.
Left-click on the front of the bin to extract a stack. Shift-click to extract a single item.
You can also use the bin while it is in your inventory. Place it in your crafting grid and you can extract stacks by pulling them from the output square. You can insert single stacks by crafting them with the bin and picking up the bin from the output square.
Items can be piped into the bin from the top, and piped out from the bottom.
If you sneak-click the bin with a Configurator it will be placed into auto-eject mode. This is indicated by green accents on the front, top, and bottom. In this mode it will pump items out of the bottom automatically.