There were two noble houses of Anjou in western France whose members were called Angevins. The first one originated with Count Fulk the Red of Anjou, son of Ingeger, in the 10th century. His descendants rose to positions of great power. His first son, Geoffrey IV (Geoffrey Plantagenet), inherited Anjou, but wasn't satisfied with just that. So he married one of the English king's daughters, namely Matilda, and then proceeded to conquer Normandy. After he got done with all that, he decided to have a son. This son, Henry II, became the first Angevin (or Plantagenet, as the English line was known) king of England. He wasn't the last, though. Seven came after him: Richard I, John, Henry III, Edward I, Edward II, Edward III, and Richard II. After that, the Angevin line assumes a new name in the form of the English noble houses of Lancaster and York.
That part of the Angevin branch also spawned royal houses in Brittany. Arthur I, a nephew of John and Richard I, became duke of Brittany in 1196. His nephew Peter I succeeded him and the rest of the Angevin line in Brittany comes from said nephew. That line eventually got absorbed into the French royal family when Anne of Brittany and her daughter both married kings of France.
Another of Fulk's descendants, Fulk V, became one of the Crusader kings of Jerusalem in 1131, and passed this power on to four separate generations after him (Baldwin III, Almaric I, Baldwin IV, and Baldwin V). The last of these kings died in 1186.
The second house started when king Louis XIV of France made his younger brother Charles the count of Anjou. Charles then married into power over Provence. Apparently sensing that Charles was on a roll, the Pope went on and gave him the kingship over Naples and Sicily as well as the title to the kingship of Jerusalem (this one was never actual, only theoretical, but was passed down through the line anyway). The new king wasn't really on a roll, though, as he lost Sicily. But y'know, he still had Naples, and that's one more kingdom than you have. His successors (Charles II, Robert, and Joanna I) retained rule over Naples and Provence until 1382. By the time Joanna I died, the house had split into two branches. One was headed by Charles III of Durazzo and his kids, Joanna II and, believe it or not, Lancelot. That side of the family retained control over the Angevin kingdoms in Italy for the most part during the contested period. The other house was pretty strong, so that was no small feat. Charles II's grandson and great-grandson were the kings of France (Phillip VI and John II), and the latter of these made his younger son the duke of Anjou. Joanna had made this gentleman her heir, so he had claim to the kingship as well, as did his successors, Louis II, Louis III, and René.
Confused yet? I know I am. But it doesn't stop.
Joanna II made Louis III and René her successive heirs, but the kingdom was seized out from under them before they got to rule by King Alfonso V of Aragón. René managed to marry into Alfonso's family and in so doing became duke of Lorraine. So now that the Spanish are involved, pretty much all of central and western Europe's got some Angevin floating around, except the Netherlands. His nephew Charles was the duke of Maine and René's heir, and he died childless in 1481.
Anjou, Maine, Provence, and the Angevin claim to Naples all passed to the French crown since the Angevins themselves were out of the picture. The theoretical claim to the throne of Jerusalem passed to the house of Lorraine.
Charles II of Naples also had a grandson named Charles Robert who went on to become King Charles I of Hungary. His son, Louis I, went on to become king of both Hungary and Poland, so that's a substantial portion of eastern Europe too, although still not the Netherlands. Louis had only a daughter, but she married long-standing Hungarian ruler King Sigismund, who later became Holy Roman Emperor. Louis had another daughter by the exotic name of Jadwiga who married Ladislas II, king of Poland.
And that's the Angevins. It's a long story indeed, and filled with Roman numerals, but we never did get around to the Netherlands. Too bad, really.
Oh, and if you just came here for the short answer, Angevin is simply a word describing things having to do with Anjou, a province in western France.
Sources: http://www.encyclopedia.com/printablenew/27893.html
http://xenophongroup.com/montjoie/anjou.htm
Now, if you will excuse me, I have a slight Roman numeral overdose. I am going to lie down.