Why does the moon drift away from earth? I once saw on TV that the moon is slowly drifting away from the earth, something like an inch a year. In relation to that the day on earth what also increase in time.
I wonder why is that?
 A: This says it concisely, when describing the effect of tides:

Gravitational coupling between the Moon and the tidal bulge nearest the Moon acts as a torque on the Earth's rotation, draining angular momentum and rotational kinetic energy from the Earth's spin. In turn, angular momentum is added to the Moon's orbit, accelerating it, which lifts the Moon into a higher orbit with a longer period. As a result, the distance between the Earth and Moon is increasing, and the Earth's spin slowing down.

In fewer words: it is the tides.
Edit: I am copying from a comment:

To show the right sign, one must show that the orbital angular momentum of the Moon actually increases with the radius - despite the decreasing velocity as the function of the radius 
  For a $1/r$ potential, $mv^2\propto m/r$ says $v\propto 1/\sqrt{r}$, so the angular momentum $L=rp=mrv=mr/\sqrt{r}\propto \sqrt{r}$ which increases with $r$. – Luboš Motl 

In addition I found this better link by googling.
A: The tidal effect was supposed to deccelerate the Earth rotation and the lost angular momentum should be transferred to the receding Moon.
But facts go on the contrary: LOD - Length Of Day is decreasing.
The Moon-Earth distance displays an increase of 3.8 cm/yr of the semimajor axis of 384,399 km. ([Williams J.G. et al, 2008])
There is an increase of orbital radius at a ratio of $2H_{0}$ as modeled here (eqs 35 and 36).
This is a surprise to many.
EDIT add (to address some concerns evident in the comments)  
Statement 1: Established theory: Any transfer of momentum is delayed only by the speed of gravity (the usual light 'c' speed). It happens in a gravitationally bound system, like the Moon-Earth, that the angular momentum is conserved.
Statement 2: It is a widespread beleif (a wish is not theory, Ok?): the Earth slows down the rotation due to tidal effects. The paper with the computations is ..., please?
Statement 3: Facts: We are recording the most precise direct measurements ever made:
 - The Moon is receding.
 - The LOD ( Length of Day ) is shorter and shorter, implying that the the Earth's angular momentum is increasing!
A choice is mandatory because it exists an internal contradition between the Statements 1, 2 and 3.
My choice is that the tidal effect must be of a low order.
The question remains: Why is the Moon receding?  
All previous studies about the past, based in proxies, shall be ignored because the inconsistency exist now, and we must seek a credible answer to explain the present time.
Those studies deserve a few words:
Eclipses - The lack of correct time keeping in the past, and imprecisions in the recorded time and location of eclipses can put to trash those studies.
Tides - the tide amplitude can be affected by several localized factors as coastal line configuration, how deep is the ocean here and there, etc,... Today, as in the past, the tide values are not uniform along the globe because the Earth is a dynamical system.  It is not enough to line up some values.  
I wonder why persists the spreading of the misconception about the LOD?
(IMO, the unpleasant answer to this is out of the scope of PSE and I will keep it to myself)

A: from Astrometric Solar-System Anomalies of Anderson and Nieto, 2009, page 9,
Increase in the eccentricity of the Moon's orbit

While the mean motion and semi-major
  axis rates of the lunar orbit are
  consistent with physical models for
  dissipation in Earth and Moon, LLR
  orbital solutions consistently reveal
  an anomalous secular eccentricity
  variation. After accounting for tides
  on the Earth that produce an
  eccentricity change of $1.3*10^{-11} yr^{-1}$ and tides on the Moon that
  produce a change of $-0.6*10^{-11} yr^{-1}$, there is an anomalous rate
  of $(0.9\pm0.3)*10^{-11} yr^{-1}$ ,
  equivalent to an extra 3.5 mm
  $yr^{-1}$ in perigee and apogee
  distance (Williams \& Boggs 2009).
  This anomalous eccentricity rate is
  not understood and it presents a
  problem.

On the anomalous secular increase of the eccentricity of the orbit of the Moon, by L. Iorio, 2011,  explores several alternatives to explain the problem. All of them were inviable, concluding:

Thus, the issue of ﬁnding a satisfactorily explanation
  for the anomalous behavior of the Moon’s eccentricity remains open.

also, from Iorio slides ON THE ANOMALOUS INCREASE OF THE ECCENTRICITY OF THE LUNAR ORBIT: SEARCH FOR POSSIBLE EXPLANATIONS , 2011, he try to offer: A VIABLE, empirical EXPLANATION

Let us assume that there is a small radial extra-acceleration of the
  form...  

This procedure is called 'data fit' and obviously it is not an EXPLANATION at all.  
I based my other answer on the decreasing LOD FACT, and all other answers are saying the contrary.
With this anser I make notice to the fact that an anomaly is present and that the present physics is unable to model it.  
Again I point to a MODEL where the reported anomaly is not present because data is along with theory (eq 35 and 36). 
I'm expecting a reception to this answer in line with the reception to the other answer.
May be the case that some doubt in your minds can rise the need to read 'out-of-the-box' and try to see if the Sun-Earth anomaly (AU increase) or the Pioneer anomaly can be explained by this model.
When we have the chance to make measures with more precision we have to report an anomaly.
A bunch of anomalies is a call for a new model.
I'm expecting that someday, somebody, will read that paper. It is a cosmological model that do not need DM, DE, Cosmological Constant, it goes well with GR, and agrees with data both at local scale and cosmological scale.   
