Q. What is a heresy?
A. Unlike apostasy, which is the complete rejection of the Catholic Faith, heresy is a partial rejection of the Catholic Faith. Any baptized person who refuses to believe one or more of the of the truths revealed by God and taught by the Catholic Church is technically a heretic. These Truths would be the dogmas of the Faith like the Doctrine of the Holy Trinity, Immaculate Conception, Infallibility of the Pope, Real Presence of Christ in the Eucharist, etc. One can no more be slightly heretical than they could be slightly dead.
The root of the word means to pick and/or choose. Meaning some things are chosen others are not, thus, the heretic does not accept all that the Church teaches but chooses to believe what is agreeable to their own way of thinking and reject other aspects of the faith that are uncomfortable or unappealing.
It should be noted that in the sin of heresy, as in every other sin, we have to distinguish between material sin and formal sin. If a person does something which is wrong, objectively-but a wrong of which he is unaware through no fault of his own is-then we say that the person has sinned materially but not formally. In his wrong action there is no personal guilt.
A Catholic who would reject a truth of the faith, who would decide, for example that he didn’t want to believe in hell, would be guilty of the sin of heresy, both materially an formally. A Protestant, however, sincerely believing teachings of the church in which he was raised and with no opportunity for knowing otherwise, would be a material heretic only; he would not be formally guilty of the sin of heresy. This is why the anathemas issued by the Council of Trent, against the various protestant heresies, are applicable to the Catholics who willfully and knowingly leave the Catholic Faith and embrace Protestantism. The anathemas are not applicable to Protestants who innocently and sincerely believe what their denomination teaches.