Ruth instigates her right to remarriage to Boaz as the next of kin by uncovering his feet. This imagery of foot uncovering (in the context of the kinsman-redeemer) comes from the Law of Moses -
Deuteronomy 25:9 (NASB)
9 Then shall his brother's wife come unto him in the presence of the elders, and loose his shoe from off his foot, and spit in his face, and shall answer and say, So shall it be done unto that man that will not build up his brother's house.
The removal of the shoe was the consequence of not fulfilling the role of kinsman-redeemer. In other words, Ruth met him with no one looking, and asked him through this non-verbal behavior to marry her "or else."
Ruth 3:10 (NASB)
10 He said, “Who are you?” And she answered, “I am Ruth your maid. So spread your covering over your maid, for you are a close relative.”
Spread your covering = marry me (in respect to Ezekiel 16:8, which is to share the covers and become one flesh). In accordance with the Law of Moses (in tandem with the guidance of Naomi who was familiar with the Law of Moses), Ruth had popped the marriage proposal with Boaz.
The response of Boaz indicates that he was already familiar with his obligation as the kinsman redeemer to Ruth. He indicates her nobleness because she did not confront him in public, where the removal of his shoe by her would have been disgraceful (in accordance with the Law of Moses). In other words, Ruth did not assume that she would have found favor in the eyes of Boaz, especially since she was a Moabite, and perhaps there was perception by Boaz that she was a woman of loose morals. For example,
Ruth 3:10-12 (NASB)
10 Then he said, “May you be blessed of the Lord, my daughter. You have shown your last kindness to be better than the first by not going after young men, whether poor or rich. 11 Now, my daughter, do not fear. I will do for you whatever you ask, for all my people in the city know that you are a woman of excellence. 12 Now it is true I am a close relative; however, there is a relative closer than I.
He did not think she was loose. In fact, Ruth was magnanimous because she was confronting Boaz in private; that is, she did not confront him in public, which he understood and appreciated. She was a Moabite, of which no male was permitted access to becoming part of Israel (Deut 23:3). That is, he understood that Ruth had wished to invoke the kinsman-redeemer obligation with him, but with discretion since she was a Moabite widow (and perhaps would have found no favor in the eyes of Boaz).
In summary, the foot-uncovering was the gesture by Ruth to invoke her kinsman-redeemer right to marriage to next of kin. As a Moabite widow, she confronted Boaz in such a way, that if he had no favor for her, the confrontation would have been unknown and undiscovered: Ruth had no intent of shaming him in public in accordance with the stipulations and allowances permitted by the Mosaic Law. However, Boaz's response indicates that he understood the gesture (of uncovering the foot). Also his immediate response was that another relative stood in the way, and so he understood the gesture as relating to that relative. That is, at the end of the story, Boaz got his closer relative to uncover his foot (removed his shoe) in order to forfeit his right to Ruth.