The cost function is a function of the unknown parameters \( \boldsymbol{\Theta} \) where the latter is a container for all possible parameters needed to define a neural network
If we are dealing with a regression task a typical cost/loss function is the mean squared error
$$ C(\boldsymbol{\Theta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta}\right)\right\}. $$This function represents one of many possible ways to define the so-called cost function. Note that here we have assumed a linear dependence in terms of the paramters \( \boldsymbol{\Theta} \). This is in general not the case.