Grave sin is just that it is a sin that is of a grave or serious manner. Some examples of grave sin would be murder, adultery, idol worship, apostasy, all sexual intercourse outside of the bond of marriage, stealing, lying under oath, bearing false witness, etc. There are more that fit the category of mortal sin, but that list is pretty long.
The primary passage that we see in Scripture a differentiation between the gravity of sins is in the first Epistle of St. John where he writes: 1JN 5:16 If a man knows his brother to be guilty, yet not of such a sin as brings death with it, he should pray for him; and, at his request, life will be granted to the brother who is sinning, yet not fatally. There is a sin which kills; it is not over this that I bid him fall to prayer. 17 Sin may be wrong-doing of any kind; not all sin is fatal. So here we see St. John speaking of two types of sin indirectly. Those sins that do not bring death, we can pray for the forgiveness of our fellow Christians; but those sins that are fatal or brings death with it, we should no pray for.
St. Paul in his letter to the Galatians writes: GAL 5:19 It is easy to see what effects proceed from corrupt nature; they are such things as adultery, impurity, incontinence, luxury, 20 idolatry, witchcraft, feuds, quarrels, jealousies, outbursts of anger, rivalries, dissensions, factions, 21 spite, murder, drunkenness, and debauchery. I warn you, as I have warned you before, that those who live in such a way will not inherit God’s kingdom. Notice the last sentence in this passage. It is a warning that St. Paul gives to Christians (he is writing to the Christians of the church in Galatia) that those who do these things will not inherit God's kingdom.
The best way to look at this is that even in our secular judicial systems we separate crimes into two categories felonies and misdemeanors right? Felonies which are more grave criminal acts usually have much harsher penalties than misdemeanors. The same follows in the Justice and Judgement of God, which our secular judicial systems mirror. It doesn't make sense for a society to send someone to jail for 20 years for driving 10 miles over the speed limit; nor does it make sense for us to only fine a murderer $100-200 either. Neither of these scenarios, would be considered just punishment would it? Both acts due to their gravity require differing penalties, and we intuitively perceive the justice in that.
