Biography of Mahlon

Ruth 1

1 Now it came to pass in the days when the judges ruled, that there was a famine in the land. And a certain man of Beth Lehem of Judah went to sojourn in the country of Moab, he, and his wife, and his two sons.

2 And the name of the man was Elimelech, and the name of his wife Naomi, and the name of his two sons Mahlon and Chilion, Ephrathites of Beth Lehem of Judah. And they came into the country of Moab, and continued there.

3 And Elimelech Naomi's husband died; and she was left, and her two sons.

4 And they took them wives of the women of Moab; the name of the one was Orpah, and the name of the other Ruth: and they dwelled there about ten years.

5 And Mahlon and Chilion died also both of them; and the woman was left of her two sons and her husband.

Ruth 4

9 And Boaz said unto the elders, and unto all the people, Ye are witnesses this day, that I have bought all that was Elimelech's, and all that was Chilion's and Mahlon's, of the hand of Naomi.

10 Moreover Ruth the Moabitess, the wife of Mahlon, have I purchased to be my wife, to raise up the name of the dead upon his inheritance, that the name of the dead be not cut off from among his brethren, and from the gate of his place: ye are witnesses this day

From Jewish Encyclopedia, by Emil G. Hirsch and Gerson B. Levi

A son of Elimelech and Naomi, the Bethlehemites who emigrated to Moab because of the severe famine in Judea (Ruth i. 2). This might have been the reason for the name "Chilion" (wasting), as also for his brother's name "Mahlon" (disease). In Moab, Chilion married Orpah (ib.), and, after living in that land for ten years, died there.E.

From Wikipedia on Mahlon and Chilion

In the Book of Ruth, Mahlon and Chilion were two brothers, the sons of Elimelech of the tribe of Judah and his wife Naomi. Together with their parents, they settled in the land of Moab during the period of the Israelite Judges. Mahlon married the Moabite woman Ruth while Chilion married Orpah (according to the Midrash, Ruth's sister).

Elimelech and his sons all died in Moab, leaving Naomi, Ruth and Orpah widowed. Naomi returns to Israel, but advises her daughters-in-law to stay in Moab; while Orpah takes the advice, Ruth chooses to stay with Naomi and convert to Judaism. In Israel, she then takes part in levirate marriage---marrying a relative of Mahlon's, an act which will ensure that Mahlon's name is not forgotten, as any child she has will be considered as if it were Mahlon's child. She marries Boaz, and her child, Obed (biologically Boaz's but counted as if Mahlon's), becomes the paternal grandfather of King David.