The Call can be characterized in a number of different ways.
At its core it is essentially whatever attracts an individual to The Old Ones and The Cult in the first place.
"To hear The Call" is to find oneself drawn to Cthulhu and His Cult, often persistently. It is a nagging to delve deeper and find out more.
This, however, is a surface representation of The Call.
The true Call goes much deeper.
A brief overview of The Call can be found on the website here.
Here is what The Bible of Cthulhu has to say about The Call...
The Call can sometimes be a bright burn where, as soon as one learns of The Cult of Cthulhu, they feel home and plunge themselves forward, while at other times it can be dim and unclear.
Following The Call is the responsibility of each individual, so that they may discover their potential, Awaken and Ascend.