The GS50 and TFS50 are designed to be used in conjunction with either standard audio amplifier or dedicated subwoofer amplifier. Most users will find connecting to a standard amplified speaker output to be easiest and sufficient. However, using a dedicated subwoofer amplifier will yield the optimal bass performance but disable the satellite speaker capability. Dedicated subwoofer amplifier produces superior, cleaner bass sound because the amplifier is only amplifying a pre-filtered low frequency signal. When connecting to a regular amplified speaker output, the amplifier is amplifying a full range of frequency and the subwoofer's built-in crossover suppress (but not fully filter out) the mid and high frequencies upon receiving the full amplified signal. The subwoofer will sound inferior when being listened to on its own as you may hear some mid an high frequencies coming through. However, the real-life difference may be negligible when being listened to with the entire sound system.
To learn more about picking the right specification of amplifier, please read this article "What amplifier should I get to match my speaker?"
If you are buying a dedicated subwoofer amplifier, the same power handling and impedance load requirement is applied as standard amplifier. In addition, you should look for a subwoofer amplifier with crossover level control for optimal customization to suit your musical preference.