Your question implies that you already have a pretty good idea of the difference between heterochromatin and euchromatin in terms of both structure and function.

In the past few years, the highly organized, compact heterochromatin has moved from being viewed as the packaging or encapsulating of "dead" (unused) DNA to a more important role as creating different types of compact DNA with distinct features and functions. One of the most intriguing roles of heterochromatin might be to protect the genome from being overcome by "parasitic" mobile elements of DNA. But we are still left with your question...

Let's consider an experiment: If you take a gene that is normally expressed in euchromatin and you place it in a region of heterochromatin, it ceases to be expressed. The gene is said to be "silenced." The difference in gene expression is an example of something called a "positional effect;" that is, the activity of a gene depends on its position along a chromosome. Also, the ends of chromosomes (the telomeres) as well as the centromeres are discrete functional regions of the chromosomes, even though they do not encode transcribed genes. Typically, these regions are highly organized as heterochromatin. Now let's consider what heterochromatin is -- I referred to is as "highly organized" but what does that mean? Typically, heterochromatin is physically "organized" on platforms of proteins that recognize and bind the DNA, creating a compact architecture.

Okay - consider all of this together. First, why do only certain regions bind the proteins? Why not all along the chromosome?

There must be some sort of "address" or "indicator" along the DNA that mediates the binding of the proteins. In fact, I used the word "recognition" in the above scenario. It is thought that specific, "hallmark" sequences of DNA designate a region for heterochromatin. It turns out that there are some general rules for predicting this, though the rules are not absolute. In general, euchromatin tends to be GC rich while heterochromatin tends to be AT rich. And telomeres and centromeres, which have distinguishing features in terms of sequence, clearly are distinct from the rest of the genome.

An interesting aspect of this is that heterochromatin can be "dynamic" -- changing during development or differing from cell to cell. Another intriguing area of investigation is how the heterochromatin is perpetuated from mother cell to daughter cell or even from gamete to embryo. It is a bit too complicated to get into via email, but there is lots out there on this really "hot" topic in molecular and cellular biology. Dive into it if you are interested! And keep asking questions.