Series wiring: amp to coil#1 +. Coil#1 - to coil#2 +. Coil#2 - to amp. Makes 1 continuous line. For series, you add the ohms, so coil#1 = 8ohm + coil#2 = 8ohm, so whole speaker = 16ohm. Not very loud.
Parallel wiring: amp to coil#1 +, coil#1 + to coil#2 +. Amp to coil#1 -, coil#1 - to coil#2 -. Looks like a ladder, 2x lines with coils in the middle. For parallel you divide the coil ohm by number of coils, 2. So coil#1 = 8ohm, /2 = 4ohm total. Much louder.
Bridging is tieing both left and right channel together on one speaker output. Most commonly it's left channel + and right channel -. Many times this simply doubles possible output power, so 20w + 20w (L+R) would be 40w to the speaker. However, in high current amps its a little different. I have a high current amp that's 20w x 20w, but when bridged is rated at 223w.
When bridging, ohms are very important. If your load (speaker) is 4ohm, because you are bridged, you are basically in parallel with the amp, so 4 /2 = 2ohm. If your amp is not 2ohm stable, you'll fry it.
Home audio often uses 6ohm or 8ohm speaker outputs, so having 2x coils parallel would be a 3ohm or 4ohm load, amp would be 1.5ohm or 2ohm. Not healthy. Wiring 6ohm coils in series would be a 12ohm load, bridged the amp would see 6ohm (12ohm /2). Quite acceptable and nominal.
That's if the home audio is bridgable, many are not. Bridging is usually relegated to car audio amps as home audio will not tolerate the low impedance.