The gene that typically makes a chicken blue is partially dominant and suppresses black pigment. That means that if a bird has 1 copy of the gene, then it has the black only partially suppressed, making it look blue. If the bird has 2 copies of that gene, then the black is nearly completely suppressed, making it white with only a few black feathers, that is called splash. No copies of the gene produce a black bird. So, black and splash both breed true (both are homozygous).
There is another way to get a blue chicken, and that involves a gene that is recessive to black. This gene never creates splash, only black or blue, and if 2 of these blue birds are used as parents, all of their progeny are blue. This is called self-blue or lavender.
If you see a chicken referred to as "BBS", that means Blue/Black/Splash, the first (and more common) variety. The cool thing about partially dominant traits like BBS, is that you can reliably know the exact genetic make up (genotype) from the appearance (phenotype). That is not true with recessives (like the self-blue), pure black birds can carry the self-blue and pass it along for generations with no indications at all, then a particular pairing can suddenly throw 25% blues.