I understand that a torrent minimizes the server load by using other participating members to fetch content. One thing I am confused about is, the different parties are connected through the server anyway, therefore complete stress of Data exchange would fall on the server anyway. At best, disk seek will be reduced.
What design architecture of torrent servers actually solves the issue mentioned above?
Using the BitTorren protocol, the purpose of the server (aka tracker) is only to manage the clients in a way they can find each other. The actual data transmission happens between the clients only (that's peer-to-peer, p2p).
Basically, a client asks the server about other clients which are currently getting the same torrent (file(s)), and the tries to connect to these clients and does the actual data transmission. Thus, the server load is quite low because the server only needs to know about the clients which download the file, but is not involved with the actual data transmission at all.