A continuous edge means that the slab is able to transfer load to the adjacent slab through that edge. Consider the above L shape building with three slabs cast monolithically (this is important, because, even if you have a slab adjacent to the first slab the edge would not be continuous if they are not physically connected. The edges should be connected in such a manner that moment could be transferred between them).
The edge common to slab 1 and 2 is a continuous edge, similarly the edge common to slab 2 and 3 is continuous. Rest are discontinuous edges.
Again, keep in mind that you have to detail (i.e. provide reinforcement) and cast (construct) the slab in such a manner that you make the edge common to the two slabs continuous.
In the above figure even though Slab-A and Slab -B have common edge that edge is only continuous in first case where the reinforcement is also continuous.