Hello there,
My understanding of the two is as follows:
Material Heresy is simply when one who holds the Christian faith but denies any article of the faith that has been defined and taught by the Catholic Church (dogma). For example, if you were to deny the Immaculate Conception, you would be in, at least, Material Heresy.
Formal Heresy is when you willfully, and with knowledge and understanding, reject an article of the faith as taught and defined by the Catholic Church. Formal Heresy is far more severe because it is done with knowledge and understanding that the particular thing denied is taught by the Church and yet the position is held with obstinance.
Basically, when Material Heresy is committed alone, it is usually a mistake done in innocence or ignorance, but Formal Heresy is malicious because it is done willfully and with intent.
Examples:
If a poorly catechized Catholic denies the existence of Purgatory, but does it through ignorance or misapprehension and with no intent to disobey the Church, he would be in Material Heresy, but not Formal Heresy (because he did not know that such a thing was heretical nor did he have intent to disobey the Church). Of course, he might be guilty of not bothering to learn his faith, but he would not be guilty of Formal Heresy. If he had known what the Church teaches about Purgatory, and yet insists that there is no Purgatory, then he is in Formal Heresy.
A Catholic who knows and understands what the Church teaches about salvation and yet decides that salvation is by ‘faith alone’ and then subsequently leaves the Catholic Church, has committed Formal Heresy.
If you had a Southern Baptist who was born and raised in his Protestant church with no knowledge that his church’s teachings were heretical, then he would be a material heretic, but not a formal heretic. If he, on the other hand, knew and understood that the Catholic Church teaches otherwise then he would be a formal heretic.
If you had a Protestant that is a militant anti-Catholic that knows and understands what the Church teaches about Mary, for example, and yet willfully rejects those teachings, he is a Formal Heretic.
It should also be noted that heresy differs from apostasy in that heresy is a denial of some points of the faith, but not all. Apostasy is a denial of the Christian faith entirely. One who left the Catholic Church and became a Muslim would not be a heretic, he would be an apostate.
Also it should be noted that those that are separated from the Roman Pontiff, but yet, do not deny any article of the faith are schismatics (and are neither, necessarily, heretics or apostates).
Heresy and apostasy are both sins against Faith and very grave. Schism is a sin against Charity and is also grave, but not as bad as the former two.
Pax Domini sit semper tecum!