Tyrek Lannister is a cousin of Jaime and Cersei Lannister. His father was their uncle and is now dead. The Lannisters always strove for power and position and Cersei got Robert to make two of her cousins, Tyrek and Lancel Lannister, his squires.
House Hayford is a noble house from the Crownlands. It is sworn to King's Landing. The only Hayford living is Ermesande Hayford, a female baby, who is the last of her line. She was in King's Landing and survived when the rest of her relations died in the War of the Five Kings. The Lannisters knew that who ever married her would get claim to her lands. They quickly married her to Tyrek, so he would get lands and titles. Tyrek was thirteen at the time, while Ermesande was still nursing.
The other squires teased Tyrek terribly about this. They call him "Wet Nurse", and ask him what color swaddling his bride wore on their wedding night. Tyrek was in the royal procession that saw Myracella of at the docks. When Joffrey caused the riot, Tyrek was caught in it and didn't get back to the castle. Tyrion and Varys sent out men looking and offered rewards, but no-one came forward with information. He is presumed dead after disappearing, the most common theory is that he was beaten and stripped and the body thrown in the river. Tyrion regrets that they couldn't find Tyrek, as his father was Tyrion's favorite uncle.
Still as no-one knows for sure, little Ermesandre is not officially a widow yet. Though it has been said that when Tyrek's death becomes official, she will be the first one to become a widow before she is weaned. The people of Hayford are happy that the marriage makes them safe from continued war. Jaime Lannister is assured that lady Ermesandre bends the knee for King Tommen, or at least she will, when she learns how to walk.