According to Merriam-Webster, the meaning of cultivate is:
1 : to prepare and use (soil) for growing plants
2 : to grow and care for (plants)
3 : to grow or raise (something) under conditions that you can control
So when you cultivate your values, you grow/care for them, deepen your understanding of them and strengthen them. So when you say, for example, “He cultivated his love of his family”, you’d mean he deepened and strengthened his love for his family, working on his love to make it better.