"Change of heart" means that someone has changed their mind. It is usually reserved for important or big decisions that may involve emotion.
For example, if Gregory wanted to study history but changed his major to engineering, you would say he had a change of heart. If Mary planned to move to another country but decided to stay in her hometown, you would say she had a change of heart.
"Change of heart" can be used for more minor decisions, as well, but in that case, it would sound more appropriate to just say they "changed their mind".