What Did Jesus Mean in Matthew 15 and Mark 7?
The Corban Supplanted God's Law
In Matthew 15:6, Jesus says the Pharisees teach a Corban / Korban payment allowed a son to say to his parents 'with what I may have profited to you has been given to the Temple.' What did Jesus mean?
Jesus said this oral teaching by the Pharisees violated the written command to 'honor' one's parents. Jesus meant that the Law commanded the duty to not allow one's parents to slip into poverty (where this exists we will discuss momentarily), and the Pharisees supplanted this Law by excusing a son from such a duty if he promised to give his money to the Temple instead, i.e., as a corban / korban (offering).
The Law's command to honor one's mother and father -- one of the ten commandments -- was always interpreted to require support of one's parent if they fell into poverty. See Thomas F. McDaniel, Ph.D., New Testament Aramaic Names and Words and Shem Tob’s Hebrew Gospel of Matthew (2008) at 25. For a direct link, see: http://tmcdaniel.palmerseminary.edu/Volume4_ShemTob+.pdf
Hence, the Pharisees were teaching that you could avoid having to support your parents if they fell into poverty as long as you gave money to the temple. Obviously, they were negating the law to their own advantage, as they were likely authorized to skim from the monies given to the temple.
For a first century stone with the Hebrew letters "KRBN" - meaning "korban," see this link from bible-history.com.
See also "Korban," Wikipedia.
In the case of Mark 7:11, Jesus addressed the case where a man says to his parents that the financial support, which he should be giving them as a demonstration of his honoring them as required in the Torah, has instead been declared by him to be a Korban / Corban. Once the vow was made the man had a religious basis for denying his parents the kind of financial support they needed. The religious authorities place greater authority in the proclaimed Corban than in the commandment to honor one’s parents. The reason for this prioritizing of the Corban above the Torah was obvious: the man’s financial benefits covered by the Corban were given to the temple for use by the religious authorities, rather than to the man’s parents.