horizontal scaling refers to partitioning data in such a way, that parts of data are placed on different servers (which is opposed to vertical scaling, when the same server gets more capacity)
In horizontal scaling data is partitioned in such a way, that parts of data are placed on different servers. This is required when it is no longer possible to fit data into the same machine / server / db. In search applications this type of scaling is often referred to as sharding. This is opposite to vertical scaling, when the servers already in use are made more powerful (by adding more CPU cores / RAM / disks etc).
Horizontal scaling is aimed at copying with growing data set, while vertical scaling is aimed at growing user base (more users asking content from the same server / shard).
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