What the Torah Says
The Torah says, in the context of introducing the commandment of "Sefirat HaOmer," the following: (Vayikra 23:9-14)
"And G-d gave this instruction to Moshe, to communicate: Speak to the Children of Israel and say to them, 'When you enter the Land which I Am giving to you, and you harvest its crops, you shall bring the "Omer," (the Omer is a dry measure, containing the volume of 43.2 average eggs. It is the amount of barley flour that had to be brought, and is also the name of the offering) the first of the harvest, to the Kohen. And he shall move the Omer forward, backward, right, left and up-and-down, before G-d, as an expression of your free will, on the day after the 'Shabbat,' shall the Kohen move it in the manner described."
"And you shall make, on the day of the ritual movement of the Omer, a lamb, unblemished, in its first year, as a burnt offering to G-d. And its associated grain offering should be two tenth-"ephahs" (another dry measure) of fine barley-flour mixed with oil, a burnt offering to G-d, with a pleasant aroma, and its libation of wine, one fourth of a "hin" (a liquid measure). And you shall not eat bread, nor roasted kernels, nor full kernels, until this very same day, until you bring the offering to your G-d; an eternal statute for all of your generations, wherever you may live."
Some Words of Explanation
There are five types of grain; they are:
"Chitin" - Wheat
"Seorim" - Barley
"Kusmim" - Spelt
"Shibbolet Shual" - Oats
"Shifon" - Rye
There are two categories of "age" of these grains:
"Yashan" - "Old"
"Chadash" - "New"
The definitions of "Old" and "New" in this context depends on when the plant took root. If it took root prior to the Sixteenth of Nisan, the Second Day of Passover, in a given year, then subsequent to the Sixteenth, it is considered "Yashan," Old. Prior to the Sixteenth, it is still considered "Chadash," New.
If the grain took root after the Sixteenth of Nisan, it is not considered "Yashan" till the following year, after that year's Sixteenth of Nisan.
What is the practical application of all this?
The practical application is that there is a dispute among the authorities on Halacha, Jewish Law, as to whether these laws apply outside of the Land of Israel, where they certainly do apply. Some say they do not apply in the Diaspora; others (including the Gaon of Vilna, one of the greatest of modern (18th Century) authorities), say that the laws do in fact apply.