First off there are many labor theories of value, this is just a basic basic overview. Karl Marx did not invent the labor theory of value, he added to it, and applied it to his economics, Adam smith and David Ricardo had different versions, even Aristotle, St Thomas Aquintes and as far as Benjamin franklin had theories based on the labor theory of value.
The basic theory is that the value of a commodity is based on the labor put into it, so origionally you have raw materials and capital, those things are bought at a price generally also based on labor, and then you mix it with labor, which creates the added value of the commodity. So basically the value is all the material value that went into creating the commodity PLUS the value.
Now when we say value, we are talking about an objective measure, we are not talking about what people as individuals value certain thing (so maybe value is'nt the right word), we are talking about a basic point on which exchange values are based, you could say its what commodities would be priced if supply and demand are at equilibrium.
A commodity are things, (when we are discussing the LTOV) which are consumer goods (many would include services, as would I) and valued based on their use value. So for example, a hat is a commodity, and its value is based on the fact that you can wear it and keep your head warm and so on and so forth, but if you have a hat that was given to you by your father before he died that was his favorate hat you are not going to sell that hat for the market prices of a regular hat, that price will not be a commodity price, you have added sentimental value, the LTOV is NOT talking about that, its NOT talking about stocks and bonds, which are not commodities they are loans and non material capital, it is NOT talking about pieces of art who's value is sentimental, the LTOV is talking specifically talking about commodities based on use value.
Now when you put supply and demand in the mix you get price, so for example a bottle of water is generally not that expensive in a competative market, and it generally has a low labor value as well, but when your at a music festival, where you have a supply and demand situation totally out of whack and you'll have prices much higher, the LTOV is NOT talking about that.
So why is the labor theory of value important? Well it gives you an idea of a basic price that supply and demand will derive the market price from, and it also (especially when it comes to Marxian economics), shows the source of value and profit.
Many opponents of the LTOV like to bring up the buggy vrs a car example, i.e. a carriage and a car take a similar amounf of labor to produce, yet most people weould value a car more, Sure, but go out and buy a carriage, lets say your a movie producer or a collector, and you want a carriage, its gonna cost you, because as demand dropped so did supply, but the price is STILL based on the labor time, which will be significant.
Any time, the market value drops below the labor value of a product, it will stop being produced.
You can basically track this overtime, the supply and demand of computers has'nt changed that significantly overtime, as more computers have been made more people have wanted them, but the prices have dropped, why? productivity means that it can take less labor to produce a computer, the same is the case with most commodities, (in this sense the supply and demand is effected by the Labor value, in the sense that productivity increases allow for more potential supply, meaning less labor time is used in production per unit).
Now what do we mean when we say labor? We mean all muscle and brain power put into the production, So software production is not just printing the CDs, is finding the concept, writing the code and so on. This gets rid of the argument that neo-liberals have in their constant and desperate defences of capitalists when they say "But the bosses also contribute a lot, they come up with ideas and so on," YES, sometimes they do, and that is included, but whether of not their compensation is based on their labor is the subject of a different discussion.
So as Industry develops ways to produce MORE per hour of labor, even if the supply and demand is the same, the price will drop, because the value has dropped.
The implications of this theory are different, but for Marxists, and most Socialists, the implication is that of exploitation, the Capitalists profit is derived from extracting excess value from labor, along with other implications. However for other economists its implications are different, such as propertarians arguing that the value created from labor insinuates ownership of land for example.