If you were to ask many for the definition of a sin unto death they would not be able to explain it.

1 John 5:16-17 If anyone sees his brother sinning a sin which does not lead to death, he will ask, and He will give him life for those who commit sin not leading to death. There is sin leading to death. I do not say that he should pray about that.
17 All unrighteousness is sin, and there is sin not leading to death.

To answer the question what is a sin unto death one must put himself in the situation or thinking of the apostles.

As you study the moral Laws of God found in the whole Bible you will note that some are what we refer to as death penalty offences. Murderers, kidnappers and homosexuals are put to death under God's unchanging moral Law. Even those who do not understand just what the New Covenant is should not argue that those sins are done away.

When you read about sins unto death understand that the writer is pointing back to the sins he understood were death penalty offences in the Law. Also realize that the Bible is extremely simple to search to find sins that are unto death or death penalty offences. There is no guess work to find what the scripture teaches are "sins unto death".

Gospel Minutes.org