"So he married Gomer daughter of Diblaim, and she conceived and bore him a son." NIV translation
Hosea believed and obeyed so he married Gomer. She must have been known in the area as an adulterous woman (probably a prostitute) because God did not tell him the name of the woman he was "to take to yourself". Can you imagine the gossip that must have broke out when this respectable man went and took this woman to be his wife? In spite of all of that, he obeyed and we, as Christians, are called to that same extreme obedience to the Lord.
"Then the Lord said to Hosea, 'Call him Jezreel, because I will soon punish the house of Jehu for the massacre at Jezreel, and I will put an end to the kingdom of Israel. In that day I will break Israel's bow in the Valley of Jezreel.'" NIV translation
This may seem different to us as, when we choose names for our children, God is pretty much left out of the process. But, throughout the Bible, we can see that God had parents give their children a specific name for a specific purpose. God is in charge of even the smallest details and our freedom is in letting Him handle it. So, the child is to be called Jezreel which means "God plants" and this child is to be a sign that God is going to punish Israel for this event.
The massacre that is referred to can be found in 2 Kings 10. Ahab was the king of Samaria (his wife was Jezebel) and the palace was in the city of Jezreel. Ahab did evil and the prophet Elijah was sent to confront him and Ahab repented. God then said that the punishment of the people would not occur during Ahab's lifetime but during the time of his children. After Ahab died, Jehu, the king of Israel, massacred the people of Jezreel and did it to show how loyal he was to God. God did not tell Jehu to do this; it just seemed right to him and consistent with the prophecy of Elijah.
"Gomer conceived again and gave birth to a daughter. Then the Lord said to Hosea, 'Call her Lo-Ruhamah, for I will no longer show love to the house of Israel, that I should at all forgive them. Yet I will show love to the house of Judah; and I will save them-not by bow, sword or battle, or by horses and horsemen, but by the Lord their God.'" NIV translation
Now we see the picture of unfaithfulness as Gomer has a child from an adulterous relationship (she cheated on Hosea). God told him to name the girl Lo-Ruhamah which means unpitied or unloved. The girl is an example of Israel's adultery with other gods and He says that He will no longer pity or love them. Has God's mercy ran out? The simple answer is no but there is a big lesson in here for us today. God's grace is sufficient and there is no place where that grace cannot touch you (as seen in the testimony in the link). But, you can keep on sinning in the face of God until the day that you no longer hear the Spirit inside you calling you to repentance. Its not that God's grace cannot reach you its that you are unable to hear and receive that grace.