I have already hooked up the regular speakers and power to the amp, now I just want to add a headphone jack. It says to wire the grounds from both speakers together, then to the jack, and to wire the left and right audio points to it directly. Can someone explain what the "wire to internal speaker" points mean? I know it sounds simple, but for instance what are the arrows for? They look like diode symbols to me (I thought this because they could have easily done without the arrows).
This kind of jack allows left and right speakers to be connected when no headphone plug is inserted (top image).
Upon inserting a headphone plug, both speakers are disconnected by mechanical force of the plug forcing both switch contacts to open. Output current is directed only to headphones, allowing private listening to the headphones only (bottom image).
The lines with the arrowheads represent switch contacts. You would connect your speakers to those terminals, and they would be turned off when you plug your headphones into that jack.
The jack you show in your scienceshareware link is a mono or single channel jack - it won't handle both channels of stereo. From the photo, I can't tell whether or not it has a switch contact - if it has three solder terminals, one will be a switch contact.