Matthew 13:24 Jesus gives the meaning of this parable in verses 36-43. All the parables in this chapter teach us about God and His kingdom. They explain what the kingdom is really like as opposed to our expectations of it. The kingdom of heaven is not a geographic location, but a spiritual realm where God rules and where we share in His eternal life. We join that kingdom when we trust in Christ as our Savior.
Matthew 13:30 The young tares (weeds) and the young blades of wheat look the same and can't be distinguished until they are grown and ready for harvest. Tares (unbelievers) and wheat (believers) must live side by side in this world. God allows unbelievers to remain for a while. At the harvest, however, the weeds will be uprooted and thrown away. God's harvest (Judgment) of all people is coming. We are to make ourselves ready by making sure that our faith is sincere.
Matthew 13:33 In other Bible passages, leaven (yeast) is used as a symbol of evil or uncleanness. Here it is a positive symbol of growth. Although leaven looks like a minor ingredient, it permeates the whole loaf. Although the kingdom began small, and was nearly invisible, it would soon grow and have a great impact on the world.
Matthew 13:40-43 At the end of the world, angels will separate the evil from the good. There are true and false believers in churches today, but we should be cautious in our judgments because only Christ is qualified to make the final separation. If you start judging you may damage some of the good "plants!" It is more important to judge our own responses to God than to analyze others' responses.