From DT Online
The melting point of most metals is lowered when it is mixed, or Alloyed with another element or impurity - just as spreading salt on ice will cause it to melt. Careful mixing of the alloying elements can lead to a range of Alloys of the same constituent metals with different melting points (e.g. Hard, Medium and Easy Silver Solder).
There is one particular proportion which creates a mix having the lowest melting point possible for that Alloy. This is known as a Eutectic Alloy. This special mix not only has the lowest melting point but also changes from liquid to solid at a fixed temperature - the Eutectic Point.
Low melting point Alloys are useful in Casting for example, since less energy is needed to melt the metal, and the instant transformation from liquid to solid makes Eutectic Alloy very useful in soldering and brazing.
Non-Eutectic alloys solidify over a range of temperatures first passing through a semi-solid ‘pasty’ stage which becomes increasingly thick until it finally solidifies. This can be useful if the semi-molten alloys has to be worked in some way. Alloys of equal parts Lead and Tin or 70% Lead and 30% Tin, can be seen from the Phase Diagram to pass through a ‘pasty’ stage which is why traditional plumbers used these compositions of solder for their ‘wiped joints’ - a process rarely used today.