Molar heat of fusion of ice?
Your interpretation is correct.

The molar heat of fusion is the amount of heat necessary to melt a mole of ice at its melting (or freezing) point. That means, to get 1 mole of water from 1 mole of ice at its melting point (0 degrees Celsius) it would require an input of $6.01\ \mathrm{kJ}$. 

The conceptual reasoning is that it requires so much energy to break the bonds and allow more motion (but not completely).

Conversely, $6.01\ \mathrm{kJ}$ would be released upon the freezing of water at that point (1 mole of water anyway).