Well, Dido was a princess of Phoenicia, when she was married to Sychaeus, who was probably the weltiest man of the area.
They hadn't been married for a long time yet and were very happy with each other when Pygmalion, Dido's brother, became king. Now you must know that Pygmalion was very jealous of Syaeus' gold and had him murdered. In the mean while, he spread the rumour that Sychaeus was on a long journey and tried to calm Dido. But no matter how much he searched he could not find the secret tresure chamber.
Then the gost of Sychaeus came to Dido in a dream, told her all the evil things Pygmalion had done and told her where the tresure chamber was. She got the gold, rallied all the people who were sick of Pygmalion's tyranny and sailed away to find a new country for her and her people.
When she came to North-Africa, she asked the king of the Nomads if he would sell her a piece of land. He promised her she could have as mush land as she could stretch a cowskin around. Clever as Dido was, she cut the cowskin into fine pieces and and thus, was able to get enough land to built her city.
The king -charmed by her cleverness- asked her to marry him, but she declined, saying that a second marriage would feel like unfaithfulness to Sychaeus whom she'd promised her love forever...

And that's not even what caused her to kill herself... Want me to tell you about her relationship with Aeneas, or do you wanna discuss this first?

Anyway, I first have to tell you a little bit about Aeneas to make the story more clear...
Aeneas was a Trojan. I think you all know what happened to Troy...
During the night Troy fell, Aeneas had had a dream in which (the dead prince) Hector warned him about the Horse, told him to flee the city and said that he was destined to built a city by the Gods. Upon waking up, he found the city under attack and tried to flee with his family. Aeneas was able to escape with his father, his son and a group of people. Sadly his wife did not make it out of the burning city.Thus began his journey, together with his friends and family.

But whereas Jupiter and Venus (Aeneas' mother) rooted for him, Juno did everything to stop him from reaching his destiny... So when he was over halve way of the journey, Juno arranged for a storm to blow him of his course.
He ended up on the coust of Carthage where he -seperated from his men because of the storm- wandered around. His mother, Venus, saw that he neede a helping hand and placed herself, disguised as a shepherdess and told him of Cathage and Dido's history.

When he found his men back and word of them spread through out Carthage, they were invited to the palace to have a banquet. There he told his story.
But during the time he was telling the story of his travels, Cupid -disguised as Aeneas' son- was shooting love arrows at Dido, causing her to fall in love with Aeneas.
During the course of the next days, Dido went to seers, hoping they could inform her of Aeneas' feelings for her and what she should do. In the end, Anna, Dido's sister, told her to go for the relationship and she did. They had an affair of a year.
But then the Gods urged Aeneas to leave again and go built his city. It left Dido heartbroken. She had her sister built a pyre, under the pretense she wanted to burn all of Aeneas' stuff. But instead of burning his stuff, she burned herself...