A Wave is symbolized as one of the strongest forces on earth. So it symbolizes strength. Also if you read more into it, its about faith. A wave is you against mother nature, you cannot control it, you just have to put your faith into her.
The girl's father was passing away in the hospital and the last thing he did was write a letter to her mother-- and at the end it read: "Tell morgan I love her." She got it tattooed in his handwriting in memory.