Symbolism, Imagery, Allegory
There are surprisingly few symbols in Tom Jones, especially given how long the novel is. We think that part of the reason for this relative lack of symbols is that Fielding keeps emphasizing the importance of realism and believability in fiction. Literature that relies heavily on symbolism—on objects and images that actually mean something else—tends to be less strictly realistic than what Fielding appears to be going for here.
Still, there is clearly one thing in the novel that symbolizes Tom and Sophia's love for one another: Sophia's fur muff. (A muff is a tube of fur or fabric that women used to use to warm their hands back in the day.) Mrs. Honour is the one who first points out the deeper meaning of Sophia's muff, when she tells Sophia that she spotted Tom kissing it and calling it "the prettiest muff in the world" (4.14.11). Obviously, Tom is using the muff as a stand-in for Sophia herself.
After hearing this romantic story, Sophia buys into the whole muff-as-symbol thing wholeheartedly. When her muff accidentally falls into the fire, Sophia grabs it straight out of the flames. Her passion to save her muff convinces Tom that Sophia must have feelings for him. So this muff (or at least, the feelings it symbolizes) is what brings our two love-struck main characters together.
The muff reappears twice more: at the inn at Upton, where Sophia discovers that Tom is sleeping with Mrs. Waters, she bribes a maid to stick the muff in Tom's room somewhere where he will spot it. Tom finds the muff and realizes that he just missed Sophia, and that she is probably angry with him. And when Tom refuses Arabella Hunt's attractive proposal of marriage in Book 15, Chapter 12, he takes out Sophia's muff and kisses it to affirm his loyalty to her. Each time, the muff stands in for Sophia and for the relationship between the two.
Now, the big question: why a muff, in particular? It is a pretty common object that Sophia would probably have carried around with her a lot, so it's a convenient, believable thing for Tom to notice about his ladylove. It's also a physical object, so Tom can kiss it whenever he's thinking about Sophia (which happens surprisingly often in the narrative).
But beyond the explanation of simple convenience, there is a somewhat ruder interpretation. We'll just come out and say it: the slang term "muff" (to mean a woman's pubic hair) was in use even back in the 1740s. We are pretty sure that Fielding specifically chose a muff to symbolize Tom and Sophia's love because (a) the pun is lewd and funny, and (b) it emphasizes the sexual tension between the two characters early on in their relationship, which builds up our suspense about when these two crazy kids are going to get together.