Your speakers sound like they have biwire terminals for speaker wire. This is designed so you can use double speaker wire back to your receiver or amplifier.
This means that you will need some kind of receiver or amplifier to play them. TVs made of the last few years do not have the ability to play speakers without additional electronics. You will probably need a receiver with the correct type of connection to get the audio from your TV (usually Toslink optical). You will also need to connect the two red and two white terminals as well as to the receiver unless you use a biwire speaker hookup.