I have a set of items, each of them with a grade and a price. On this set, a partial order is defined where x <= y if grade(x) <= grade(y) and price(x) <= price(y).
I have items like price(x) = 3 , grade(x) = 1 and price(y) = 2, grade(y) = 3. I don't understand how these should be ordered. Please help me!
Remember that in a partial order, two objects don't necessarily have to be comparable; maybe $a\not\le b$ and $b\not\le a$!
That's what happens here. By definition, $x\le y$ iff $grade(x)\le grade(y)$ and $price(x)\le price(y)$. In the specific case you mention, the grade of $x$ is lower than the grade of $y$, but the price of $x$ is higher than the price of $y$; this means that $x$ and $y$ are not comparable.
On an abstract level, you're seeing a way to combine two partial orders to get a third. If $\le_1,\le_2$ are two different partial orderings on the same set $X$, then their intersection - $x\le_3 y$ iff $x\le_1y$ and $x\le_2 y$ - is also a partial ordering on $X$. You're looking at the intersection of the "price" and "grade" partial orderings. (And there are lots of other methods for building new partial orderings from old.)