If I'm not stepping on Malcolm's toes here, the "~" symbol denotes the connections for alternating current (a.c).
A full-wave bridge rectifier always consist of four diodes connected in the configuration as shown in the sketch, and its job is to change (rectify) an alternating current into a direct current (d.c). On the d.c. side of the bridge, you simply connect the "+" (Cathode) terminals to the battery positive and the "-" (Anode) terminals to the battery negative.
The output of most every battery charger is already rectified for d.c. but the clever thing with the bridge is that is ensures the output always remains the same with respect to positive and negative, regardless of how the battery charger is connected. In other words, the two wires from the battery charger can be connected any way around to either of the "~" connections, but the positive output from the bridge will always be positive and negative output will always be negative. In essence, you can be safe in the knowledge that you will not damage your battery, regardless of how you connect your battery charger.
A typical 25-Amp bridge might look similar to that in the sketch. The physical size will vary depending on how much current the bridge is designed to handle, and therefore can become warm in use. Some even have a metal plate attached to the underside - the idea being that the metal plate should be bolted to a larger metal surface in order to dissipate the heat.
Here in Blighty, it's simply pronounced as "AC/DC". Down there in Oz, now you know why Angus Young pronounces it as "Akky-Dakky".