What I am primarily currently learning about is hyperbolic geometry and methods to find hyperbolic structures on triangulated manifolds. I see phrases such as 'cusp ends' and 'manifold with one cusp' in many, many places but I cannot seem to track down a thorough, formal definition of what it means for a manifold to have a cusp. The only use of the term cusp I am familiar with is for example for the singularity of the curve $y^2 = x^3$.
Any book references which would contain information relevant to me (in general) would be appreciated also.
Thank you.