Question

What is latent heat of fusion?

Answer 1

There's two forms of latent heat, there's latent heat of fusion which is melting, and there's latent heat of vaporization which is boiling. They describe the direction of energy flow when changing from one thing to the next like solid to liquid, or liquid to gas.

Answer 2

If you have a lump of solid at its melting point ... like ice at 32°F ...
you have to put a certain amount of heat into it just to change it
to water at 32°F.  That amount of heat, that's used just to change
a solid lump into liquid without changing its temperature, is called
the heat of fusion for that substance.

The number is different for every substance.

For water, it takes 336 joules of heat to melt 1 gram of ice
into 1 gram of water, all at 32°F (0°C).
That's an enormous latent heat of fusion ... more than almost any
other known substance.  That's why ice is such a good choice
when you need something to put in your drink to cool it down.
Ice absorbs a huge amount of heat before it melts and the drink
gets watered down.