The answer to this question can be found in chapter 16 of The Giver. Jonas actually asks what the Giver's favorite memory is, but then he quickly backpedals and says that the Giver doesn't have to give it to him yet. 

"What is your favorite?" Jonas asked the Giver. "You don't have to give it away yet," he added quickly. "Just tell me about it, so I can look forward to it, because I'll have to receive it when your job is done." 

The Giver responds by saying that he would be happy to share his favorite memory with Jonas. The memory that he shares is a memory of a family at Christmas time. The memory contains a fire in the fireplace, candles on the table, snow falling outside, and lights on a tree that is inside the house. Jonas finds that last detail a bit odd, but that doesn't stop him from thoroughly enjoying the general feeling of the entire memory. Jonas witnesses the family sitting together and enjoying the company. The Giver asks Jonas what he felt, and Jonas describes two specific things. He explains that he felt "warmth" and "family." Jonas also says that he experienced a third feeling that he can't quite describe. The Giver tells him that the feeling is love, and the concept is completely new to Jonas.

"I certainly liked the memory, though.  I can see why it's your favorite. I couldn't quite get the word for the whole feeling of it, the feeling that was so strong in the room." 

"Love," the Giver told him. 

Jonas repeated it. "Love." It was a word and concept new to him. 

What is The Giver's favorite memory in The Giver?

The Giver’s favorite memory is a family celebrating Christmas.

In Jonas’s community, there is no such thing as family or love.  The elderly are kept separate from everyone else until they are euthanized.  Families are a thing of convenience, created by committees.  When Jonas begins to learn about the memories, he starts to see that there was a time when people had emotions and cared about one another.

One day, Jonas asks The Giver what his favorite memory is.  He tells him that he does not need to give it to him yet, because he wants the old man to keep it as long as he can.  The Giver tells Jonas that he will give it to him.

He was in a room filled with people, and it was warm, with firelight glowing on a hearth. He could see through a window that outside it was night, and snowing. There were colored lights: red and green and yellow, twinkling from a tree which was, oddly, inside the room. (Ch. 16)

Jonas asks The Giver to explain what he saw.  The Giver tells him that he is seeing grandparents, and the emotion he experienced was “love.”  This is an emotion that simply does not exist in Jonas’s society.  They do not have any strong emotions, but they also do not have any strong connections to other people.  The concept of grandparents also does not exist.  The parents never see their children after they are grown, and the children never even meet the parents’ parents, because there is no point.  They have no relationship with their children once their children are grown.

Jonas says that it is a dangerous way to live, and the man asks what he means.  Jonas is not sure.

He could feel that there was risk involved, though he wasn't sure how.  "Well," he said finally, grasping for an explanation, "they had fire right there in that room. There was a fire burning in the fireplace.  And there were candles on a table. I can certainly see why those things were outlawed. (Ch. 17)

Jonas is focusing on tangible things, because he cannot quite put his finger on the real danger in the intangible things in the vision.  He has been taught all of his life that emotions are dangerous, yet they are celebrated in this memory.  Jonas focuses on the fire and candles, but the real danger is the fact that everyone in the old memory cares about one another and the strong emotions they feel as they celebrate the holiday.

Despite the fact that he thinks the way of life in the memory is dangerous, Jonas tells The Giver that he appreciates the warmth in the room.  He goes home and asks his “parents” if they love him, and they react in confusion and amusement.  They do not know love. They do not understand the emotions that Jonas has, and that people used to have.  The Giver is showing Jonas how the world was, and the benefits of it.  People used to have families.  Now they have family units.