Equilibrium concentration is noting but the final concentration which remains unchanged after equilibrium is achieved.

for example if you are studying any heavy metal removal process then carry out the trial experiment for long time and at some point of time your final concentration will not change and that is your Ce. while calculating adsorption capacity you can take final concentration as Ce like for kinetics study.

You will get this value by successive trials. You have to measure periodically the concentration of the solution in contact with the adsorbent (stirring in a hermetically closed vial is strongly recommended). You'll see the concentration decrease with time, first quickly, then slowly, and after a given time (generally less than 24h for a few mg to a few tens of mg of adsorbent), the concentration will become low and perfectly constant. This is the equilibrium concentration. Once the time required for getting it is known, you can do the same with different concentrations and build the corresponding adsorption isotherm (to which you can apply different models, such as Langmuir, Freundlich, etc.).

Alain

A model paper is attached to understand the use of equilibrium concentration to calculate the amount of equilibrium adsorption, % of sorbate removal and adsorption isotherms.

its simply the final concentration of the adsorbate in solution, when there is no change in concentration observed against time.

The concentration equilibrium (Ce) can be calculated by measure the variation of concentration against time. When no any change of this concentration can be observed, this starting point of concentration stability is Ce. You can read this paper related to Ce calculation: http://www.tandfonline.com/doi/abs/10.1080/19443994.2012.692036

In addition to above answers, you just allow a known conc. (Co) of solute stand in contact with a known quantity of  absorbent until equilibrium is attained. Then you find the conc of the solute left in the solution using any appropriate analytical method, this will give Ce and the difference between Co and Ce will give you qe the amount absorbed. Thanks

Equilibrium concentration is the concentration that no any change may be observe after various measurements during adsorption process. 

A complete guidance ..

https://youtu.be/wWIZyxrp04I

The simple and straight answer follows:

Equilibrium concentration (Ce) = Abs./Molar extinction coefficient

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Calculate the Molar extinction coefficient easily in a few clicks:

https://www.youtube.com/watch?v=rdj058lMyHU