The bacterial strains that carry fertility factor (F) are called F+ cells. They have the ability to donate that F. The bacterial strains that lack this F are called recipients and are designated F–. The fertility factor exists as a plasmid, a circular DNA physically separated from the chromosomal DNA.
An Hfr strain is the one in which this F (plasmid) gets integrated into the chromosomal DNA. This strain has the ability to promote a high frequency of recombination.
In general, all cultures of F+ cells have a small proportion of Hfr cells. These Hfr cells can transfer the markers from the host chromosome to a recipient cell during conjugation.