When Samsung and LG released their curved OLED TVs (and later on curved LCDs as well), a lot of people didn't understand why is that good for. Most reviewers and consumers seem to prefer a flat design - which means you can hang the TV on the wall and it looks better.
It seems that there's still a lot of confusion here, and today LG Display published an article that explains the advantages of curved TVs (it also details the company's flexible OLED technology). According to LG, there are several such advantages. First of all, the Curved OLED TV can enhance the viewer’s immersive experience with its curved form. The screen "wraps around the viewer" and so there's a comfortable feeling of stability and immersion. LG explains that the curved screen has a curved trajectory similar to a person’s ‘Horopter Line’ allowing the maintenance of a constant focus.
The second advantage is the distance to the viewer is constant (unlike a flat TV in which the middle is closer than the edges). This means that in a flat TV there's a subtle image and color distortion which does not happen in a curved panel. The larger the flat screen and the closer the distance from the screen, the distortion becomes more noticeable.
The final advantage is that a curved screen feels larger and brighter compared to a flat TV. This, again, enhances the viewing experience. LGD says that a viewer will feel that the size of a curved TV screen is larger than its actual size. Curved OLED TV also feels brighter because the light coming from the screen is focused on the center of the screen.