Could someone explain in layman's terms what the scientific terms
solidus and liquidus are please?

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Clarification of Question by mihilism-ga on 07 Oct 2005 03:45 PDT

Are they in between the solid and liquid states or something?

Solidus 

During heating, solidus is that temperature at which an alloy begins
to melt. Between the solidus and liquidus temperatures, the alloy will
be a mixture of solid and liquid phases. Just above the solidus
temperature, the mixture will be mostly solid with some liquid phases
(like the consistency of snow, but hotter!). Just below the liquidus
temperature, the mixture will be mostly liquid with some solid phases
(like sleet).

Liquidus 

Liquidus is the temperature above which an alloy is completely molten.
In other words, when an alloy exceeds the liquidus temperature, there
are no solid phases present. The alloy is completely melted and
flowing.

http://www.wallcolmonoy.com/TechServices/NicrobrazNewsArchives/WCC_Article_Solid_Liquid.htm

Just a comment to point out that the concepts mikewa explained in his
comment are not restricted to alloys and metals.  Any compositionally
variable system will have solidus and liquidus curves.  For instance,
the mixtures of silicate minerals that make up the Earth's mantle
begin melt over a range of temperatures;  melting begins when the
temperature reaches the solidus, but is not complete until the
temperature reaches the liquidus.

The key here is that the system must have at least one degree of
compositional freedom.  The solidus and liquidus for a pure substance
are identical, and a pure substance melts completely at a single
temperature (for a specified pressure).