Cable plug tool for Di2
Shimano's TL-EW300 Cable Plug Tool is one of those tools that you only use when building or maintaining your bike. It allows you to securely and properly connect and disconnect EW-SD300 electric wires, connecting your Di2 components to each other.
While you could actually plug in and unplug the older EW-SD50 Electric Wire by hand, doing so with the newer EW-SD300 wires is not recommended. The wires are simply too small to grab properly. You're far more likely to twist and break these wires doing it by hand.
Plugging in Di2 connectors correctly requires more force than you'd expect and a loose connector can cause all kinds if weird issues if you're unlucky.
When you plug in components correctly you should feel and hear a click (or 'pop').
Using the tool
Both ends of the cable plug tool are used when connecting components. One end is used almost exclusively for connecting wires in hard-to-reach places such as the front derailleur, while the other end is used whenever you've got a bit more room.
TL-EW300 vs TL-EW02
Shimano's older electronic groups do use EW-SD50 wires instead of the newer EW-SD300. These older wires are bigger and can actually be connected / disconnected by hand. Still, using the TL-EW02 tool is recommended - it's just so much easier.