The "awkward turtle" is a hand gesture. The hands are placed one on top of each other, palms down, thumbs sticking out to the sides. The thumbs are then wiggled. The intent of the gesture is to acknowledge being caught in a very embarrassing, socially awkward situation.
This hand gesture is believed to have first been invented in 2005. It is intended to relieve the tension of the awkward moment and get everyone to laugh. Plush toys representing the awkward turtle are available for sale, and as of 2014, there is even a Facebook group devoted to the awkward-turtle moments of life.