Probably my favorite character on the show, he is the distant cousin of the aristocratic Crawley family. Since British law dictates that only direct-male lines can inherit (irony there considering the royal family switches), Matthew is surprised to hear the news after the future heir dies during the Titanic.
Far more down-to-Earth than his distant cousins, Matthew does accept his destiny to be the future Earl. He makes the mistake of commenting that the family would push on his daughters on him, and then he sees Mary who overheard. He obviously likes her on first sight. But after a season, they end up not being together.
Matthew ends up dating Lavinia Swire later, and Mary tries to make the best of it.
But both ladies wouldn't see much of Matthew during his tenure fighting in the Great War, known later as World War I.
He ends up gravely wounded in battle.
And ends up without the use of his legs. Lavinia stays by his side, despite his severe blow to his self-esteem. But as he starts to get the use of his legs, his fiancee dies from Spanish Flu.
So in time, he asks Mary to marry him. Which excited most of the views, despite Mary often times, not being worthy of "happiness".
Their wedding is a big ordeal and nothing out of the normal happens.
Their marriage is mostly a happy one. The only thing that strains it for the most part is losing Downton due to the fortune being lost. Matthew inherits another fortune but it is ridden with guilt if he uses it to rebuild Robert's legacy.
Robert offers a compromise, Matthew invests in the estate, and him and Robert are equals on all matters of the household.
At the end of the third season, he finally has his own son. He is so thrilled and filled with joy over the whole thing.
And dies from a car accident after being so "happy" and not paying attention. In truth, Dan Stevens wanted to leave the show, and they had to kill him off. Which is something he still apologizesfor to this day.