Chalav Yisrael is milk that was watched by a Jew when the cow was milked to ensure kashrut.
The Mishna in Avodah Zarah (35b) says "the following articles of heathens are prohibited but the prohibition does not extend to all use of them: milk which a heathen milked without an israelite watching him, ..." The Gemara there explains that this is becuase a non-Jew may have substituted a non-Jewish animal, or mixed in non-kosher milk.
Among the later poskim, Rabbi Moshe Feinstein ruled that it was permissible to drink milk that was milked by large non-Jewish dairies in countries like the United States, because the government regulates the production of milk, and imposes penalties on anybody who sells the milk of other animals as though it were cow's milk. People who follow Rabbi Moshe Feinstein will therefore drink any milk that is available for purchase at a supermarket, and this is the common custom in the United States. (This milk is called chalav stam, or chalav hakompanies)
There are other people (in the United States) who do not drink chalav stam, for one of two reasons.
There are people who follow Rabbi Moshe Feinstein's ruling that chalav stam is permissible, but prefer to be stringent. These people keep chalav yisrael as a minhag.
There are poskim such as the Lubavitcher Rebbe, and Rabbi Ovadia Yosef who disagree with Rabbi Moshe Feinstein's ruling. They hold that decree in the Talmud is like many other rabbinical decrees that continue to be binding, even when the reason no longer applies. People who follow these poskim (many Sephardim, and all Chabad Hassidim) keep chalav yisrael as a matter of halacha.
There are a number of differences between these two positions. One difference is that people who keep chalav yisrael as a matter of halacha cannot eat foods certified as "dairy equiptment" becuase their poskim hold that when one cooks chalav stam, it makes the utensils non-kosher.