* The two candidates vied for the attention of the voters. (meaning they competed for it)
* The athletes vied for a spot on the Olympic team. (meaning they competed for it)
* The restaurants on the street vied with each other for the best view. (meaning they competed for it)
* The flowers in the garden vied for the most vibrant colors. (meaning they competed for it)
* The artists vied for the judges' approval. (meaning they competed for it)
As you can see, "vied" is often used when talking about competition. It implies a strong desire to win or be the best.