The PSR-E353 has three possible ways that it can be connected with a home theater system, depending on what equipment is in your home theater system, what kinds of connections can be used with that equipment, and how you want to use the PSR-E353 within your home theater system.
AUX IN jack -- This is for connecting an external sound source to the PSR-E353 so you can listen to the sounds coming from the external source through the PSR-E353's speakers. See page 30 of the PSR-E353 Owner's Manual. Depending on the type of audio jack on the other device, you might need to either buy a special audio cable or else use a standard audio cable with one or more adapters. The PSR-E353's AUX IN jack takes a 3.5mm (often called 1/8") stereo plug. If the audio out jack on the external device also takes a 3.5mm stereo plug, then a standard "auxiliary" audio cable with 3.5mm TRS plugs on each end should work. But if the audio out jack on the external device takes some other sort of plug, then you might need to use an adapter or a special cable. For instance, if the external device takes RCA plugs, then you might want to search the online stores for a special cable using appropriate search terms, such as "RCA stereo to 3.5mm TRS audio cable."
The PSR-E353 has two functions which specifically pertain to an AUX IN connection:
"AuxInVol" is used to help balance the sound mixture going to the PSR-E353's speakers between the external device's sound and the PSR-E353's sound. Note that you should adjust the external device's sound volume (on the device itself) first, to make sure its audio signal is strong enough but not too strong. You should also adjust the volume of, and the balance between, the PSR-E353's parts using its "StyleVol," "SongVol," "M.Volume," "D.Volume," and "S.Volume" functions as appropriate. Then you can use the "AuxInVol" function to adjust the balance between the external device's sound and the PSR-E353's sound. Finally, use the PSR-E353's MASTER VOLUME dial to adjust its speaker volume.
"SupprPan" is used to suppress part of the external device's sound, such as a vocal part that you want to sing, or an instrumental part that you want to play. First, turn on the PSR-E353's MELODY SUPPRESSOR feature. Then use the "SupprPan" function to select the left-right pan position of the sound you want to suppress. Note that the sound coming from that pan position will not be completely eliminated, just decreased, and any other sounds (which you might want to keep) coming from that same pan position will also be suppressed.
PHONES/OUTPUT jack -- This is for connecting a pair of headphones, earbuds/earphones, external speakers, or other external device to the PSR-E353 so you can listen to the PSR-E353 through the external device, or record the PSR-E353's sound using the external device. See page 13 of the PSR-E353 Owner's Manual. Again, you might need to either buy a special audio cable or else use a standard audio cable with one or more adapters. The PSR-E353's PHONES/OUTPUT jack takes a 6.35mm (or 1/4") stereo plug.
USB TO HOST terminal -- This is for connecting the PSR-E353 to a computer or other USB host device so you can transmit MIDI data to or from the PSR-E353. If your home theater system doesn't include a computer or other MIDI-capable device, then this type of connection won't be of use.