Plasmids utilize their host cell's replication machinery in order to replicate. As described in our previous Origin of Replication post, DNA replication is initiated at the ORI and may be synchronized with the replication of the host cell's chromosomal DNA or may be independent of the host's cell cycle.
Plasmids are said to be under stringent control of replication when they are dependent on the presence of initiation proteins synthesized by the host cell in order to start their own replication. In general, these types of plasmids tend to be low copy number. Conversely, plasmids that can initiate DNA replication independently of the host's initiation proteins are said to be under relaxed control, as they only require the host's replication machinery for elongation and termination. These types of plasmids tend to be high copy number.