What does the symbol $\sum_{\mathrm{cyc}}$ mean?
It means you add up over the variables in play. For example, if the original expression had $a, b, c, d$, you'd add up over those, e.g., $\sum_{cyc} a^2 = a^2 + b^2 + c^2 + d^2$.
More interesting is when you have expressions such as $\sum_{cyc} ab$ which in the context of a problem with $a,b,c,d$ would generally mean
$$ \sum_{cyc} ab = ab + bc + cd + da$$
I'm not sure if this convention is set in stone, but it's a useful shorthand. Be sure to evaluate it in context.