Question
From the book of Ruth, I know that Boaz is a form of Christ. But what exactly
is a kinsman-redeemer?
Answer
Here are the basics. Every Hebrew son would receive a part of the family's
property (usually land) as a rightful inheritance. The first-born son usually
received a double portion of the inheritance.
If a married man died without any children, there was a law that obligated
the closest kinsman (usually a brother of the man who died) to marry the deceased's
wife and redeem his brother's name and family. And if she bore a son, that child
would be considered the son of the deceased family member, receiving his inheritance
and name.
In the case of Naomi, there was a closer blood relative (or kinsman-redeemer)
than Boaz. This kinsman was happy to buy (or redeem) the land from Naomi, but was
not willing to marry Ruth (which was considered somewhat of a low-life act). He was
probably afraid that if Ruth had a son that survived all of his sons, his estate
could be transferred over to Naomi's family. (Talk about complicated family
politics!)
On the other hand, Boaz loved Ruth so much; he committed himself to being
Naomi's (and Ruth's) kinsmen-redeemer and goes above and beyond the call of duty.
In the end, Naomi is considered better off than a woman with seven sons.
Just as Boaz was Ruth's kinsman-redeemer, Jesus Christ is our kinsman-redeemer. 
That is why Boaz is a "form" or "model" of Christ. For instance, mankind was in a hopeless
condition because of sin. But God loved man so much that He desired to pay the price
(or redeem) man from their sinful state. Therefore, God sent His only begotten Son
to be our kinsman-redeemer (John 3:16). When Jesus became a man,
He thereby became a kinsman to all mankind, and therefore eligible to redeem all mankind
(Heb 9:11-14). Jesus (like Boaz) was also willing to redeem us
(Heb 12:2). And the fact that Jesus was free from sin (or the need
to be redeemed Himself), qualified Him to pay the redemptive
price (Heb 7:24-27).
Therefore, the book of Ruth is not just a great story of a man who really loved a woman,
it is also (and more importantly) the "Good News" of God who really loves us.