Jesus was continuing His teaching to the disciples, not to seek their own importance (Matthew 18:1-5), and not to despise the 'little ones' (both children and everybody who trusted Him and submitted to His authority as the 'children of His kingdom' - Matthew 18:10).  He then reinforced that teaching, emphasising that everybody is precious to Him, with this parable.
 
The imagery would have been easily understood in a farming economy.  Sheep were living investments.  They came to the owner of the flock without cost – they were born on his land.  However, it cost a lot of time and effort to raise them until their greatly increased value could be realised, in wool and milk, and as meat.  Every animal which strayed was precious and well worth searching for.  A lost sheep would not only be at risk of death from accidental injury or predators like wolves, but the farmer would lose his investment.
 
So the owner himself would keep looking for the animal until he found it.  Whatever it cost, his successful rescue mission would be the cause of great joy; a special bond would be formed with that sheep.  That is Father God's reaction too when those who belong to Him are brought back.  God cares deeply about all the people born on His world and is not willing for any of them to perish (2 Peter 3:9).  That is why Jesus came, to bring many children to enjoy God's glory (Hebrews 2:10): also to delight God as He establishes a relationship bond with them (Luke 15:7).  
 
But note: this rescue is not described as being of benefit to the sheep, but for the benefit of Father God who regains real ownership of what belongs to Him.  It is a common mistake to assume that God's salvation is primarily for the benefit of the saved.  Yes, there is great benefit: but that is small compared to God's joy when He re-establishes His Lordship over His creation.  Christians, who merely revel in the blessings of salvation, may be tempted to abuse the grace of God; but mature believers know they have been rescued at great cost, and so they have an obligation to live in such a way that pleases God (1 Corinthians 6:19-20).