The pretty, snobbish girl on a gray horse that Tom Riddle was with when he rode past the Gaunt family shack (“My God, what an eyesore!”) (HBP10).
Harry and Dumbledore are examining memories from the Pensieve when they encounter Cecilia. They start by viewing memories of Bob Ogden when he visits Marvolo Gaunt's shack. On horses, Tom Riddle and a "very pretty girl" ride past the Gaunt shack, which is when they enter the memory.
"Cecilia" is related to the Roman name, Caecilius, which was derived from "caecus" or "blind." This could be a reference to how Cecilia is unaware of the Gaunt family, who would be the end of her relationship with Tom Riddle Sr.
From the Web
Apart from her name, her apparent beauty, and the fact that she rides a grey horse and is familiar enough with Tom Riddle, the heir to the Manor, to address him as "Tom", and for him in turn to address her as "darling", would indicate that they are on close, if not intimate terms. The fact that they are allowed to ride out together, unchaperoned, in the English countryside in the 1920s, would indicate that they were at least committed to each other, if not formally engaged. Her unfamiliarity with the Gaunt family would argue also that she was not from the immediate area. It is possible that Tom had somehow been involved in the war effort in the First World War, and had met Cecilia elsewhere, and was now bringing her back to see his home.
It is worthy of note, perhaps, that when Tom's body is found some fifteen years after these events, mention is made of his parents also being murdered, but no mention of wife or children is made. We know that Tom was shortly after these events spirited away by Merope Gaunt, and that he returned some time later having been married to her; it is entirely possible that, on Tom's decamping so precipitously, Cecilia had thrown him over and left.