Fresh water will melt if the air around is warmer than 32 degrees Fahrenheit. If the air is cooler than 32 degrees (like it is in your freezer), it won't melt. This temperature (32° F), is called the melting point of the water. The warmer the air is, the faster it melts.

When you add salt to the water, it lowers the melting point of the water: the more salt you add, the lower the melting point becomes. For example, some really salty water will have a melting temperature of 20°F, instead of 32°F. This means that an ice cube made of salty water will melt at lower temperature than fresh water.

Now, imagine that If you take a salt water ice cube and a fresh water ice cube out of the freezer at the same time, and put them on the counter in your kitchen, which has a temperature of 70°F. The temperature of your kitchen is 38 degrees higher (70-32=38) than the melting point of the fresh water, and 50 degrees higher (70-20=50) than the melting point of the salt water ice cube. So, the salt water ice cube melts faster!

As written this question is nonsensical: water is already liquid, and therefore incapable of melting. You could be interested in freezing(/melting) point depression, as discussed on ScienceLine here, answers #2 and 3 here, and (sort of) here, or in ice which is being melted in fresh water vs. a solution, as in here and answer #1 here.

Salt water has a lower freezing temperature than fresh water. Because it freezes at a lower temperature, it will melt more readily when above that temperature than fresh water would.

What I don't know is exactly why salt water has a lower freezing temperature than fresh water. My guess is that it has to do with the water molecules forming cage-like structures around the salt ions, which prevents the water molecules themselves from forming crystals.