A strain of plants is one that has been selected for certain characteristics. Yes, it has to do with breeding and hybridization, and seed propagation. We often use the word "variety" instead of strain.

Usually a strain is not as stable, genetically speaking, as a named variety, but there are no set rules on this. Most strains are seed-propagated, but not always, as in Jerusalem artichokes. You can give a strain a name and call it a variety.