Symmetry and fractal symmetry aren't just concepts you learned about in geometry class (or heard about on a certain Frozen soundtrack). They are represented throughout the natural world. In really beautiful ways.
An object is symmetrical when it's not affected by a transformation (like reflection or rotation). Think: your face in the mirror or an orange slice or a butterfly. A fractal harnesses a specific type of symmetry: self-similarity. So fractals have repeating patterns that appear similar over different - albeit finite - scales. Think: snowflakes and romanesco broccoli.
Why should we care about symmetry in nature? Well first off, symmetry is amazing. And beautiful. And maybe we feel more alive in the presence of beauty. (Maybe.) Secondly, symmetry can sometimes signify functionality. For example, symmetry in knees and ankles is positively correlated with sprinting speeds. Hazah! (That's a symmetrical word.)