This term, not to be confused with the similarly-spelled "homoousios", means "of differing substance", or, more accurately, "of similar substance". It's the major component of Arius' concept that Jesus came into existence at a differing time from the Godhead. Put simply, Arius' belief was that "There was a time when the Son was not".
This concept was part of a major controversy, whereupon Arius went head to head with Athanasius and his concept of homoousios. Athanasius couldn't stomach the Arian concept, because it implied that the Son was not infinite and eternal, thus, by definition, subject to change.
He was not alone. A concept of the Son being subject to change, as opposed to an eternal constant, was very quickly regarded as a heresy by many church leaders and, in the end, such a concept was very quickly condemned.
There is an interesting ancedote to this story, incidentally, and evidence that pop culture was used to influence minds then, just as it is now. Apparently Arius had at one point borrowed the tune of a then-popular tune, replacing its words with his own, in an effort to gain support for his belief.