Horizontal Scaling means you are adding more nodes(m/c ‘s )to your cluster in order to support more load and increase performance while Vertical Scaling is increasing power of a single m/c in order to increase performance or to maintain it with increasing load by increasing (RAM,CPU)

In DB world Horizontal scaling refers to Data Sharding where the data is split into small partitions with each partition(Shard) lying in different nodes in a cluster whereas in  Vertical scaling data resides on a single node and scaling is achieved by multiple cores