Halacha in a Nutshell is a series that does not aim to actually teach you halacha. The goal is to acquaint you with the general ideas of a halachic issue so that you can follow conversations without looking like a total n00b.
For many people, an eruv is an essential "feature" of any orthodox community. From personal experience, I can tell you that it is possible to survive just fine without an eruv.
On Shabbat, one may not "carry" an item from the private domain into the public domain or between two private domains. (Note that specifically, you may not carry more than 4 amot-a measurement that is, by most accounts, approximately 6ft.) What's a public domain? That which isn't a private domain! (Don't laugh too hard, this exact definition happens in secular American law too!) In most cases, a private domain is basically what it sounds like: a building or other small, enclosed area. If you have a fenced yard, it is considered the same private domain as the inside of your house. I don't know why every orthodox Jew with a yard doesn't have a fence! Apartments are more complicated and would require their own eruv to carry between apartments. (This is my understanding based on my prior living arrangements.)
What are the practical uses of an eruv? You can carry items to synagogue: prayer shawl (tallit/tallis), siddurim, other books, toys for kids. You can also carry food, drinks, etc, between houses for meals. You would also be unable to use a stroller to take young children to shul. You can't carry those young kids either, they must be able to walk on their own. Therefore, an eruv is what frees parents (especially mothers) from the home on Shabbat when they have infants and toddlers. I only recently learned that jewelry is an issue without an eruv, and a sheitel (wig worn by some married women to cover their hair) counts as jewelry for carrying-on-Shabbat purposes.
As for terminology, you will hear that the eruv is either "up" (may be relied upon) or "down" (no carrying allowed). In most communities, an email will go out over the local email listserv near the end of the week, and there is likely both a website and phone number for status updates. If the eruv were to go down after it was checked, you are able to rely on that checking unless you know that the eruv is down. This means that if you carry on Shabbat based on an eruv status update and then learn on Sunday that the eruv went down on Friday night, you're still ok. I don't know the exact status of that as an aveira (sin), but there is a key difference in breaking a halacha when you think you're not. Reliance makes a difference, just as it often does in the secular law! Some people use this to say that you shouldn't tell other people that the eruv is down unless you are the one who checked it (in case you're wrong or they might carry in spite of the knowledge-let them sin less), but that is a questionable position. You'll hear people say it, however, which is why I mention it.
One famous eruv "controversy" you may hear about is Rav Moshe Feinstein's ruling that Manhattan could not qualify for an eruv. There are people on both sides of the issue, but an eruv still doesn't exist in the Lower East Side (Rav Feinstein's "turf," so to speak).
And for a more current eruv controversy, check out this hilarious clip from the Daily Show with Jon Stewart last week! This kind of political battle over eruvim (plural of eruv) happens in nearly every community that creates one. Also check out the post at Fink or Swim! As Rabbi Fink points out, it's very sad that a lot of the opposition comes from within the Jewish community.
The other issue with an eruv: it can be expensive. There are government permits, materials, and the time each week for someone to walk the perimeter of the eruv to check it. If you have an eruv, appreciate it and understand the work that goes into it. I think eruvim are frequently overlooked when people plan their tzedakah (charity, for lack of a better English term). Because of this, you may have a separate eruv "fee" in addition to a shul membership fee.