Twitch very rarely geo-blocks content, so accessing your favorite streams isn't a problem in general. However, for those in China, Slovakia, and other countries, Twitch itself is banned – so a Twitch VPN is essential for getting access.
If you're a streamer on Twitch, you might find that your connection lags or slows down at peak times. This could be a result of network throttling, which essentially means you're being slowed down by your ISP for using too much bandwidth. A VPN disguises your activity, and can stop this.
Finally, Twitch VPNs have been found to enable banned users to make another account, by changing IP address.