My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to errors?
A loss function is a mathematical representation of anything bad or at least undesirable: the point is that it is therefore something you want to minimise.
Calling a loss function a cost is in general just terminology designed to be simple and evocative. The intention is to appeal to your sense that cost is something you want to avoid and (specifically and crucially) that (other things being equal) you prefer a smaller cost to a larger cost.
It doesn't necessarily imply a cost in any monetary, financial, economic or business sense.
Simple examples of a loss function arise when we consider the difference between some true or correct value $\theta$ and an estimate $\hat\theta$, which you would like to be as small as possible. Possible ways of taking that further are to work with $(\theta - \hat\theta)^2$ or $|\theta - \hat\theta|$, which are both loss functions. In either case there is a minimum loss of 0 when $\hat\theta = \theta$.