Basically there are two types of coupling systems which we see in Indian Railways they are used to connect bogies with bogies & also with engine.
1)Screw Couplering: These couplers are majority in number. Presently, 90%of trains running in india have this configuration. All the blue coach train are running with these coupling system except the special CBC rake given for major trains. I will provide the video link in the CBC section
See the two picture ( 1st and 2nd ) to get an idea about Screw Couplers.
Pros&Cons...
more...

1) The Vibrations produced and jerks due to sudden acceleration and deceleration of the train are less compared to the other coupler.
2)If any of the coaches are damaged during its run the coaches replacement is possible because the any near by major junction would have a good number of their spare coaches having screw coupling configuration than the other one.
3)When a train derails due to this screw coupling which is not strong and compact in nature will make the coaches collide, climb and crash with each other and the deaths toll will be high. This is the major reason why the other coupling system came into the scenario.
Ex: Fatehpur derailment of kalka mail in which death toll was 70 badly injuring 300 others. Here the train was going at 109 Kmph.

Center Buffer Coupling (CBC): This Coupling system was being used in Railways but was not used for passenger coaches till 2000. We find this coupler in all freight train. The improved design is begin used for passenger coaches from 1998. Around 20 Coaches were imported at the beginning and later with the TOT (Transfer Of Technology) these are being manufactured in India. These coaches are found in Prestigious trains like Rajdhani, Shatabdhi, Duronto & in some recently introduced AC Express. The LHB Coaches which are used for majority of these trains have this coupler configuration. These coaches are manufactured at RCF Rail Coach Factory, Kapurthala. There are some Trains which have ICF made coaches (Integral Coach Factory ) which are blue in colour having such configuration which are being used for Important trains from year 2005. But was stopped in 2008 due tos some reasons. We can differentiate them with others as they have some indication on the side edges of a coach. see the video. ( video link )
The picture ( 3rd ) shows the typical CBC coupler used for ICF trains. The right coach which have side buffers are of no use in CBC coupling. There are made for provision of both coupling system so that they can be compatible with any configuration.
The picture ( 4th ) shows the coupler whih is present in Premium trains which is almost the same but have some mechanism which reduces the effect of jerks and has a stable design.
Pros&Cons
1)The Vibrations produced and jerks due to sudden accleration and deceleration of the train are omparitively high.
2)The replacement of coaches might be complicated as some major junctions doen't have many spare LHB coaches or CBC coupled coaches.
3) The LHB Coaches are Anti Telescopic which means they do not get turned over or flip in case of a collision which is absent in screw coupled coaches. Even though some trains having CBC system whuch are typical ICF coaches don't crash and flip but damage might be slightly high.
Example of derailment of LHB coach train. click on the link below.
click here
This accident happened when the train was at good speed nearly 100kmph.
Still the death tool was only four. If such incident had happenned with ICF train the death toll would be around 60-70. This is one of the important reason of safety which railway swtiched to these coaches. Probably by 2030 most of the major trains will get these coaches.
Note: The photos taken from internet and with due credit to given to the owners.
Excuse me if i had commited any grammatical, spelling mistakes and provided any wrong information with your kind heart.
I hope my answer reached your expections if you had any :)
Thank you,
Peace.
Source Quora. (click here
4th pic credits to /blog/post/991005/