Within the Catholic denomination, a dispensation is an exemption from Church law. For example, a married man becoming a priest being granted an exemption from the celibacy requirement otherwise imposed on all priests.
Within other denominations, a dispensation refers to a specific time period or group of people.
For example, Christians are not required to build an ark to escape flooding--God only instructed Noah to build an ark; (Genesis 6:14) "Make thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without with pitch."
Another example would be prohibitions against eating pork (Leviticus 11:7-8). In Matthew 15:11, Jesus states "Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man."
This was later reinforced in a vision from God to the Apostle Peter, documented in Acts 10.