Just I want to understand gain, power, link budget
the first thing what does gain mean


Gain is the power amplification of a system usually expressed in decibels.

Link budget, as the name implies is the power budget from one end of the link to the other and should take account of: -


Tx amplifier power lost in feeder to antenna
VSWR effects due to mismatched coax/amp/antenna
Antenna losses (especially if not bang on the optimum frequency)
Antenna gain (aka directivity) - usually a minimum of 1.7dB per antenna
Localized losses in antenna structure (usually low by design)
The actual free-space transmission loss of power versus frequency and distance
The extra losses due to fade and the fact the earth isn't free-space
The receive antenna gain
Rx mismatches and feeder losses to receiver


Lastly, you should understand that if transmitting anything you are occupying a finite bandwidth in the spectrum and that bandwidth comes with a cost - noise. Let's begin with this. The minimum power in dBm that a receiver needs to generally operate with a low bit error rate is: -

dBm = -154dBm + \$10\space log_{10}(data\space rate)\$

So if you are transmitting 1Mbps the minimal signal you'll need at your receiver input terminals is -154dBm + 60 dBm = -94 dBm.

This accounts for your receiver being at normal ambient temperatures of 300k.

Assuming you can put figures on cable losses and antenna gains and that mismatches are minimized the basic free space link loss equation is: -

Link Loss (dB) = 32.4 + 20\$log_{10}\$(F) + 20\$log_{10}\$(d) where F is in MHz and d is kilometres

This tells you how many dB are lost at a particular frequency over a certain distance in free-space (not earth). Usually, RF guys then assume it's going to be at least 20dB worse than that (margin for fading) and that in a highly populated area it will be possibly 20dB worse again. 

It all sounds a little haphazard but with care and attention to detail these equations produce very realizable systems.

I'm not going to comment on your figures because 


  let say we have 100 watt "50 dBm" transmitter connected to an
  amplifier has 70 dB gain and output power of 400 watt "56 dBm"
  connected to antenna has a gain of 15 dBi


.... makes no sense to me. I don't understand what you are trying to say.



See also other answers on this Long range (~15 km) low baud-rate wireless communication in a mountain environment (no LOS) and How to know (or estimate) the range of a transceiver?