Kan (1)
If you gather four copies of the same tile, you can declare a kan.
But that does not mean declaring kan is always the better choice.
So let us look at both the advantages and the disadvantages of kan.
1. Advantages of Kan
(1) Your fu increases
A kan gives you 8 to 32 fu, so your winning score goes up.
The 32 fu from a concealed kan of terminals or honors is especially large,
which is why people sometimes say:
“A concealed kan of terminals or honors is basically worth one extra han.”
Example 1
Pon 
Dora
This hand is a 40-fu 3-han hand worth 5200 points.
Case 1
If you add-kan the ,
20 + 8 + 16 = 44, which rounds up to 50 fu.
That means the hand becomes worth at least 6400 points,
even if the kan-dora does not hit at all.
Case 2
If instead you concealed-kan the ,
20 + 32 + 4 = 56, which rounds up to 60 fu.
Then the hand rises to 7700 points,
or even 8000 under kiriage mangan rules.
(2) You can gain more dora
Whenever a kan is declared, a kan-dora is revealed.
It is uncertain, of course, but it can also turn your hand into a huge one.
Example 2
Pon Dora
Even a hand that is only 2000 points like this
can jump all the way to haneman if the kan-dora lands cleanly.
That is probably the biggest attraction of kan.
Case
Dora
(3) You get one more draw
This is especially important not to forget when you draw the fourth tile yourself.
Example 3
Pon Draw
Here, simply tsumogiri'ing is one possible line,
but doing so means you give up one chance to reach tenpai.
If you are still aiming to win the hand, add-kan is better.
(4) Rinshan Kaihou
If you win on the rinshan tile, you gain the extra one han from Rinshan Kaihou.
This advantage only matters when you are already in tenpai.
(5) You can make a specific tile unusable for others (concealed kan only)
If you do not even want opponents to chi a certain critical tile,
a concealed kan can be effective.
2. Disadvantages of Kan
Kan always comes with drawbacks.
(1) It may increase other players' dora too
There is no guarantee that only you will benefit from the extra dora.
It may just as easily make the other players' hands more expensive.
This is especially dangerous when someone else has already declared riichi:
if you kan then, you are not only adding kan-dora,
you may also be giving them kan-ura.
(2) It reveals your value or intended yaku (concealed kan / daiminkan)
The easiest example is Daisangen.
Example 4
Pon
Even if you draw here,
you should discard it as naturally as possible.
If you kan it, becomes much harder to come out.
In online mahjong, this is exactly the kind of spot where you need the “disable calls” button.
Because if hits the table and there is a lag...
(3) It can reduce your acceptance (concealed kan only)
Example 5
Pon 
Chi 
Draw
This kind of case may be the easiest to understand.
If you conceal-kan here, it becomes a disaster.
There are other examples too,
but those are the main points.
Original Japanese page: http://beginners.biz/naki/naki05.html