How much is if my internet provider says "we have increased your WiFi connection by 2 decibels"? I understand the definition of decibel as a logarithmic unit for intensity of anything. I just cannot imagine its "actual size" when comes to the wireless connection.
Can you provide something illustrative which would help me to really understand how much it is if my internet provider says 

"We have increased your WiFi connection by 2 decibels"?

Is it a significant improvement, or is it just a trifle?
Something like some kind of a table of values (in decibels) saying that the WiFi connection is poor/fair/good/excellent withing these intervals, or anything else practical.
I mean the question like a request for explanation of the practical perception of a particular physical unit. Like if I asked "How do we perceive increasing light wavelength by 100 nm, is it a completely different color or is it almost the same?" 
ADDED:
Some asked in comments what exactly they did. It is a small square-like antenna. They physically came to my house and turned the antenna several degrees north :) to better aim their access point transmitter. And I live in a rural area. 
 A: Let me assume your internet speed is the power of the router, divided by the square of the distance from the router (as the signal is spread over the surface of a sphere with area $4\pi r^2$).
$$
\text{speed} \propto \frac{P}{r^2}
$$
Your power increased by $2\,\text{db}$ - this means a fractional increase of $(10^{1/10})^2 \approx 1.6$. With your new router you can achieve the same speed at distance $r^\prime$ as you could with the old router at a distance $r$. To find the relation between $r$ and $r^\prime$, note that
$$
\frac{P^\prime}{P} = (10^{1/10})^2 = \frac{r^{\prime 2}}{r^2}
$$
which implies 
$$
r^\prime = 10^{1/10} r \approx 1.26 r
$$
so you might get a $25\%$ increase in range, which isn't bad.
A: decibels are a scaling factor rather than a linear increase, so +2dB means the signal is *1.58 larger. +4dB would be *1.58*1.58 bigger. 2dB is a small increase, but may be just enough to improve your signal to improve your internet connection. More dB may not always give an improvement in the same way as if you stand right next to the loud speakers at a music concert you would be deafened and not receive the music as well as if you were further away where the music is a few dB quieter.
A: It means that your router has been reprogrammed to output a 58% stronger signal, given the same physical set-up this means that the signal that reach your computer is also 2 dB stronger. Note that this boost is only one way, your computer is still sending with the same power it used to. Depending on your hardware the reception may in general be better in one direction or the other, if computer-to-router was your weakest link then this change will do almost nothing to improve the overall experience.
There are two factor that compound to limit the range of your WiFi:


*

*The inverse square relation. As the signal spread out in a sphere it gets thinner with distance. Theoretically you could gain 26% more range.

*Walls and any other obstructions partially block the signal, passing through obstructions the signal will drop off exponentially. I haven't been able to find exact numbers, but I believe 2 dB would only offset a few cm of common wall.
Usually, obstructions is the main limiting factor for WiFi range in houses, so while you could quantify the extra signal strength as 26% greater vacuum range, the more relevant figure might be a few cm of plaster wall.
