Lets start with the looks, terracotta pots will never go out of style, its been around way longer then the other materials in the market as early as 3000 BCE. Terracotta pots have that patina look to it that other materials can't replace and the best part is that the longer you keep it the better it looks. 

Its natural porous nature allows for air and water to move through the walls which allows the soil to air rate faster, which helps prevent your plants roots from diseases and root rot, resulting in healthier plants.

Regardless of the weather you can use them indoors or outdoors and they still look good plus point!! is that they will not fade or discolour, better yet, if you place them outside the weather helps create that patina look to it that will add contour to your garden.

Succulents grow much better in terracotta pots, it's because of the porous nature that allows the soil to dry better and allow the roots to be healthier. Also did you know that the walls of terracotta pots naturally draw the water out for the soil on colder days which help to dry soil quicker? its important that your soil is not too wet during colder days to prevent soggy roots or root rot.