When we are talking about a "singularity", we are planning a mass with volume zero gravity surrounded by a border called "event horizon" from which nothing can escape. For there to be a black hole, somewhere must have a singularity and, for that to happen, must be enclosed on the outside by an event horizon, which means in essence that can not be seen from the outside the same singularity . Specifically, it means that there is a region unable to send signals to the outside infinity. The boundary of this region is what we call as the event horizon.
When we are talking about a "singularity", we are planning a mass with volume zero gravity surrounded by a border called "event horizon" from which nothing can escape. For there to be a black hole, somewhere must have a singularity and, for that to happen, must be enclosed on the outside by an event horizon, which means in essence that can not be seen from the outside the same singularity . Specifically, it means that there is a region unable to send signals to the outside infinity. The boundary of this region is what we call as the event horizon. 
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