Parable of the Fishing Net: Matthew 13:47-50
The parable of the fishing net is the third parable of a series of three short ones that are used by Jesus to describe the kingdom of heaven.
In context, previous to these three short parables, Jesus has just told the Parable of the Weeds which mirrors the message of this parable of the fishing net.
Jesus says, "Again, the kingdom of heaven is like a net that was thrown into the sea and caught fish of every kind; when it was full, they drew it ashore, sat down, and put the good into baskets but threw out the bad. So it will be at the end of the age. The angels will come out and separate the evil from the righteous and throw them into the furnace of fire, where there will be weeping and gnashing of teeth." (Matthew 13:47-50)
In this parable, the point is that the righteous are kept whereas evildoers are separated and thrown out. The purpose is to communicate the idea of separating the good from evil at the end on judgment day.
Beyond this point, there is no use in extrapolating the meaning. Of course, in real life, the fish that are kept would be eaten, but Jesus is not saying this about the righteous. He is only saying that they will be kept for heaven, whereas those who are evil will be thrown "into the furnace of fire."
The meaning of the parable is found in the last two verses, starting with "So it will be at the end of the age..." (Matthew 13:49-50) We are told that God's angels will separate the evil from the righteous and throw the bad into the fire for destruction.
This parable of the fishing net is a vivid description of the future judgment day, but it also serves as a warning for us to repent now while there is still opportunity. As the author of Hebrews says, "Therefore, while the promise of entering his rest is still open, let us take care that none of you should seem to have failed to reach it." (Hebrews 4:1)
For a convenient PDF/eBook version of all Jesus' parables, download Understanding the 40 Parables of Jesus Christ. This 126 page eBook also includes supplemental information for understanding these parables.