I read in fluid dynamics that the potential energy stored in the molecule of water due to the attraction by the other molecules is negative. Can energy be negative and what does it mean to have negative energy??
Potential energy is taken with respect to a reference. What we can define about potential energy isn't it's absolute value, but the difference of potential energy of two points.
For convenience and simplicity we take the the potential at $\infty$ to be $0$. And that's why for attractive forces potential is negative.
Definition: The change in potential energy of a system is defined as the negative of work done by the internal conservative forces of the system.
Absolute potential energy is undefined.Relative potential energy is defined.You are free to choose reference anywhere.
Negative potential energy is just a mathematical consequence after choosing the reference level.
Attractive forces in case of attracting molecules do positive Work that's why the change in potential energy of the system is negative.