The government is not only monitoring your e-mail. Since 9/11 the USPS has also been monitoring your snail mail for the spooks (technically, the postal service has been monitoring mail in some form or fashion for about a century). Every single letter or package shipped and/or received by the United States Postal Service is photographed and stored for varying government agencies (particularly the NSA) with access provided to civil authorities as well via special requisition (BUT NOT NECESSARILY REQUIRING JUDICIAL REVIEW!) Read more here.
Via a program referred to as Mail Isolation Control and Tracking, photos are taken of the fronts and backs (i.e., mail covers) of all envelopes and packages and stored by the NSA in what must, by now, be a very large database. Essentially, what is being collected is metadata--the data about data. For example, this method allows the NSA to keep tabs on just whom is communicating with who. And you thought that your Christmas Card to Aunt Judy and Uncle Dave were private...
While this may, prima facie, seem trivial, if one takes into account the amount of correspondence sent and received over a lifetime (just a few years even!), the NSA can map out some pretty specific details about a person. For example, one's network of friends, family, and general associates, companies with which one does business, creditors and debts, financial status, legal issues (e.g., documents from law firms and courts), personal interests (e.g., via magazine subscriptions, packages received), and much more.
For the most part, the data collection is general however we do know that specific individuals are quite often targeted for more detailed monitoring. (Think again if you believe that the government can't/won't open your correspondence and/or packages). (See a 2013 New York Times piece for some documented abuses.) Of course the government's argument is that no one can have a reasonable expectation of privacy as it relates to clearly visible data collected from the outsides of packages. This may be true, but certainly only to an extent. The extensive net of data collection and the maps that are being constructed of the lives of average American citizens with no connection to crime or terrorism IS an egregious violation of privacy. Why should your data be sitting on some government server without warrant? Most in InfoSec and the privacy field agree with me--it shouldn't!
Remailing is a method of (somewhat) obfuscating the origins of a parcel or piece of mail. For example, someone from Arizona doesn't want to give away his/her general area of residence or occupation to another party but communication is required with said party and, as such, he/she sends the correspondence via snail mail to another location to be remailed such that the postmark will show from, say, Florida instead of Arizona. Essentially, all that this requires is that one drop a pre-stamped letter into another stamped envelope addressed to a remailing service. The remailer receives, opens, and remails internal envelope.
It must be said upfront that utilizing a remailing service doesn't protect one from the purview of the USPS or other federal agencies (even the USPS offers a remailing option) if the remailer relies upon USPS. However, remailing can, in fact, be utilized to enhance one's personal privacy even via USPS as long as one understands that there is no way to avoid USPS monitoring pending one is relying upon their services. If one wishes to avoid the USPS's egregious data collection net, use a private service (no guarantees here that they aren't handing over your data as well, they likely are but using a third-party + following some simple protocols can mitigate at least some of the risk).
Remailing is just one of many privacy-enhancing options for individuals who must communicate with other individuals/companies/organizations in cases whereby physical location and/or general area of residence/occupation needs to remain private or in such cases as one wishes to remain fairly anonymous (note: a modicum of anonymity can indeed be had via remailing if certain protocols are followed). Who needs a remailing service? Some example users: abused and battered women attempting to remain hidden from the abuser, whistle blowers/leakers, people reporting crimes who wish to remain anonymous, sending complaint letters, recording ethics violations, communicating with pesky creditors/debt collectors, "secret admirers," or, more generally, simply for people who don't want to be found (and don't forget remailing is great for jokers and pranksters!)