The phrase is a metaphor, meaning it describes one thing as another to suggest a likeness. By taking the train instead of driving, she could relax and save money, killing two birds with one stone.
Pro Tip 2/3
Avoid Literal Interpretation
Don't interpret the phrase literally; it's not about harming animals but about efficiency. Joining the gym next to his office, he could exercise before work and avoid traffic, thus killing two birds with one stone.
Pro Tip 3/3
Context Sensitive
Often used in casual conversation or informal writing, not typically in formal contexts. She called her mom while commuting to catch up and save time, killing two birds with one stone.