Social ambition is the basis for the main conflict in Emily Brontë's Wuthering Heights.
Heathcliff comes to live with the Earnshaw family—found orphaned and living on the streets of Liverpool by Mr. Earnshaw. Earnshaw adopts Heathcliff and tries to give him the advantages his own children enjoy. Catherine (a wild young girl) and Heathcliff are very close as children. However, as she gets older and becomes aware of wealth and society, she drifts away from Heathcliff—trying to fit in with those who are higher on the social ladder. This bedevils the young man because he knows that he could have won Catherine's heart if he were not of common birth and/or poor. He hears conversation between Catherine and Nelly—Edgar Linton has proposed. Catherine wants Nelly (a servant—and like a sister to her) to tell Catherine if she has made the right decision. Nelly does not know—she asks if Catherine loves him. Catherine notes that he is handsome, entertaining, happy, and loves her; and...
...he will be rich, and I shall like to be the greatest woman of the neighbourhood, and I shall be proud of having such a husband.
Nelly discredits all of this, for it does not show that Catherine loves Edgar—but she does love the life she would lead ("social ambition").
Then Catherine mentions Heathcliff. (Unknown to her, he hears only the beginning.)
It would degrade me to marry Heathcliff now...
Nelly sees Heathcliff move away at this; he never hears the rest—that Catherine loves him:
...so he shall never know how I love him: and that, not because he's handsome, Nelly, but because he's more myself than I am. Whatever our souls are made of, his and mine are the same...
The second reason that social ambition is so important to Heathcliff is because of how badly he is treated by his adoptive brother, Hindley, particularly after Earnshaw dies and Hindley inherits the estate.
Heathcliff runs off (motivated by social ambition). Years later, Heathcliff returns. Somehow he has become wealthy and polished. Of him, Nelly recalls:
I was amazed, more than ever, to behold the transformation of Heathcliff. He had grown a tall, athletic, well-formed man...His upright carriage suggested the idea of his having been in the army. His countenance was much older in expression and…it looked intelligent, and retained no marks of former degradation. A half-civilised ferocity lurked yet in the depressed brows and eyes full of black fire, but it was subdued; and his manner was even dignified: quite divested of roughness...
He still loves Catherine (who is married now). It seems that Heathcliff had done all to win Catherine back, but still she is married. Heathcliff buys Wuthering Heights from Hindley (for Catherine now lives at Thrushcross Grange).
Catherine stays with Edgar and dies after becoming ill—but first she gives birth to a daughter, Catherine. Heathcliff marries Isabella (Edgar's sister), but he is an abusive husband. His wife leaves him; on her death his son (Linton) is returned to him. He also cares for his "brother's" son (Hareton) when Hindley dies.
After years of planning, Heathcliff forces Linton to marry young Catherine to get his hands on Thrushcross Grange. Ultimately, Linton dies—and Catherine and Hareton fall in love.
For all his scheming, wealth and station do not bring Heathcliff joy. He asks to be buried next to Catherine so that their remains may mingle—after all, her love was the only thing he truly ever wanted—not social status.