We never learn Mrs. Yeobright's first name. She's one of those nameless characters that always intrigue us – like the second Mrs. de Winter in Rebecca, who always stands in contrast to her predecessor. In this case, Mrs. Yeobright is herself supplanted by a character whose name we always hear, Eustacia.
Mrs. Yeobright's lack of a first name is very significant because it tells us what she is and what she isn't. She's the widow of a Mr. Yeobright, an important figure in the Egdon community; she's the mother of Clym; she's the "Aunt Yeobright" (still no first name) of Thomasin. Mrs. Yeobright is defined by her roles as a wife, mother, aunt, and leading figure in the Egdon community.
But who is the woman behind all of that? We never really get to know, though we do get glimpses of her. And the glimpses we get come largely through the very relationships that define her so completely as "Mrs. Yeobright," oddly enough.
First, we have her odd relationship with her niece Thomasin. Mrs. Yeobright is never overly warm towards Thomasin. In fact, she even thinks how she never "expected" all that much from her niece (4.4.42). Thomasin herself seems wary of her aunt. But we do get glimpses that Mrs. Yeobright genuinely loves her niece and thinks of her as a daughter in some ways.
Moved by an uncontrollable feeling as she looked upon Mrs. Yeobright's worn, wet face, she ran back, when her aunt came forward, and they met again. "O – Tamsie," said the elder, weeping. "I don't like to let you go." (2.8.43)
Mrs. Yeobright keeps a very tight lid on her emotions, though they do sometimes escape, as we see in this scene with Thomasin. Mrs. Yeobright also is very proud, which makes for a bad combination at times. She antagonizes people and she can come across as totally uncaring and even mean.
"O Clym! please don't go setting down as my fault what is your obstinate wrong-headedness. If you wished to connect yourself with an unworthy person, why did you come home here to do it? Why didn't you do it in Paris? – it is more the fashion there." (3.5.31)
Yet another facet of Mrs. Yeobright's character is revealed – her very snarky sense of humor. The woman can rip someone to shreds verbally, but she can be pretty darn funny while doing it. In some ways she's like the less restrained and more diplomatic voice of the narrator, who often makes fun of the characters with very dry commentary (check out the "Narrator Point of View" section for more on that).
It's things like Mrs. Yeobright's sense of humor and her obvious love for her son that make her loneliness and her eventual death very sad. These things all come together to create sympathy for her character, who often does what she can to make people feel very unsympathetically towards her.
As we saw with her snobby remarks to Clym about Eustacia, Mrs. Yeobright can be kind of mean (albeit funny). But her rants against Eustacia are also very revealing. They let us see just how deeply Clym's "rebellion" is affecting Mrs. Yeobright and just how close her relationship is to her son. Mrs. Yeobright is almost frighteningly close to her son, to the point of being co-dependent on him. Her life revolves around Clym to such an extent that she doesn't know how to act when he disappoints her, or ever goes against her wishes for him. She largely blames Eustacia for everything that Clym is doing to disappoint her:
"If it had not been for that woman you would never have entertained the teaching scheme at all."
Clym looked hard at his mother. "You know that is not it," he said.
"Well, I know you had decided to attempt it before you saw her. But that would have ended in intentions. It was very well to talk of, but ridiculous to put it practice." (220.127.116.11-31)
But she also gets angry at Clym and tries to pretend that she doesn't care about her son when she's actually just hurt. Perhaps more than any other character in the book, Mrs. Yeobright uses words as a shield, to deflect and hide her true feelings. So it's fitting that we learn the most about who she is as a person in scenes with no dialogue, where she's alone.
No sooner had Yeobright gone from his mother's house than her face changed its rigid aspect for one of blank despair. After a while she wept, and her tears brought some relief. During the rest of the day she did nothing but walk up and down the garden path in a state bordering on stupefaction. (3.6.21)
Mrs. Yeobright's pride and stubbornness cost her dearly here and these are flaws that she shares with Eustacia. In fact, these two women have a huge amount in common, which is probably why they don't get along at all.
First, we can see how similar Mrs. Yeobright and Eustacia are in terms of physical presence and in terms of how others perceive them. Check out these weirdly similar descriptions of Mrs. Yeobright and Eustacia:
The philosophy of [Mrs. Yeobright's] nature, and its limitation by circumstances, was almost written in her movements. They had a majestic foundation, though they were far from being majestic; and they had a groundwork of assurance, but they were not assured. (3.3.113)
The only way to look queenly without realms or hearts to queen it over is to look as if you had lost them; and Eustacia did that to a triumph. (1.7.12)
There's an element of dispossessed royalty in both of these women; the heath seems to have robbed them each of their "rightful" place in the world. In a way, Mrs. Yeobright is exactly who Eustacia might have become had she survived and remained married to Clym. Clym, meanwhile, as Mrs. Yeobright scathingly pointed out, is "just like his father," i.e., not socially ambitious (3.2.21).
We can also see how similar these women are in terms of their behavior – both are arrogant and prideful; both have tempers and hold grudges; and both are very emotional and tend to overreact to perceived threats.
And the two main ladies have very strong feelings towards Clym and effectively compete over him. Clym isn't so much a loved individual as he is a symbol of victory for each of these women. Mrs. Yeobright felt she had "succeeded" when Clym went off to Paris and Eustacia hoped to "succeed" when Clym took her back to Paris. Neither of these women fully accepts Clym as he is on the heath.
Mrs. Yeobright's estrangement from her son and her death are made even more tragic by the fact that she causes a lot of her own problems, which is a major theme in the book. Mrs. Yeobright is strongly tied to the novel's themes of love and family, and the very difficult and heartbreaking nature of families.
Finally, it's worth taking a look at the contrasting death scenes between Mrs. Yeobright and Eustacia, who is herself a Mrs. Yeobright by the time of her death. While Eustacia dies on a dark and stormy night, Mrs. Yeobright dies on a brutally hot summer day. Why set a death scene on a sunny, summer day? Well, in this case, light seems to play a metaphorical role in Mrs. Yeobright's end – light represents both truth and especially exposure here. Mrs. Yeobright thinks she sees the "truth" about her family's feelings towards her, and she dies in despair.
The "how" of Mrs. Yeobright's death is also notable – she's bitten by a poisonous snake. A snake, of course, was in the biblical Garden of Eden and tempted Eve to take some fruit from the Tree of Knowledge, so it's definitely interesting that Mrs. Yeobright was killed by a snake shortly after discovering certain truths about her son and his wife. And, at the very moment of her snake-induced death, Mrs. Yeobright learns that her son wasn't angry with her after all.