I had the same thing happen to my house. I bought it in 2011 for 137,000, which was the same as the FHA appraised value (because FHA won't guarantee a loan for more than their appraiser thinks its worth). January of last year, I get the letter from the tax office and see that my house has been assessed at only 122,000. I was shocked too, until I read a similar document that Phil told you to read.
The short of it is, no matter what the tax assessor calls their calculation, it is an assessment. It was mass-produced along with everyone else's in your neighborhood by looking at its specs on paper (acreage, house square footage, age, beds/baths) and by driving by your home to see its general condition. The fact that your lawn may be less well-kept than the last time they drove by could have affected the decision a little. It's very unlikely to have been a major determinant of the assessment.
The assessment value affects taxes, and taxes only. It is, in most states, a matter of public record, and so it could be used by a potential buyer to negotiate a lower price. However, everyone in the housing business knows that the assessed value is not the market value, and the buyer's agent will be encouraging their client to make a more realistic bid.
This "assessed value" is not an "appraisal value". An appraisal is done by someone actually walking into and through your home, inspecting the general condition inside and out, to try to make a fair evaluation of what the home is actually worth. That number is almost always going to be more than the assessment value, because it takes into account all the amenities of the home; the current fixtures, the well-kept (or recently-replaced) flooring, the energy-efficient HVAC and hot water system, etc etc. It also takes into account recent comparables; what have other houses, with the same general statistics, the same amenities, relatively close in location, sold for recently?
That will still generally be different from the true market value of the home. That value is nothing more or less than what a potential buyer will pay to have it at the time you decide to sell it, and that in turn depends 100% on your potential buyers' myriad situations. Someone may lowball even the assessed value because they're looking for a deal and hoping you're desperate; you just reject the offer. Someone may be looking at comparables indicating the house is maybe overpriced by $10k. You can counter and try to come to an agreement. Or, your potential buyer could work five minutes from your house, and be willing to pay at or above your asking price because the next best possibility is another 10 miles away.
Since you aren't looking to sell the home, none of this matters, except to determine any escrow payments you might be making towards property taxes. Just keep making your mortgage payment, and don't worry about it. If you really wanted to, you could petition the state for a second opinion, but you think the value should be higher; if they agree with you, they'll raise the assessed value and you'll pay more in taxes. Why in the world would you want to do that?