1. 崭露头角的；萌生兴趣的
If you describe someone as, for example, a budding businessman or a budding artist, you mean that they are starting to succeed or become interested in business or art.

2. 刚起步的；新出现的
You use budding to describe a situation that is just beginning.

1. reproduction of some unicellular organisms (such as yeasts) by growth and specialization followed by the separation by constriction of a part of the parent