욕심 is related to greed, but not the same. We tend to use it in a much less negative sense.
욕심 is wanting too much of something, like a desire, strong wish, ambition, or aspiration, but not necessarily selfishly.
It describes aggressively desiring something, and is not always negative in connotation like "greed".
욕심이 많아 가지고 (not 욕심히) alludes to having a strong desire to obtain or achieve something. It is closer to strong motivation or drive than greed.
As another example, 일에 대한 욕심 means wanting to achieve too much in your work - usually a good quality.
Here are some other words related to 욕심, greed, passion, etc.
- 탐욕 = greed.
- 욕망 = desire.
- 욕구 = (bodily or physical) craving.
- 열망 = passionate yearning; (mental) craving; desire.
- 열정 = passion; fervor.
(욕 = desire, craving, 심 = heart, mind, 탐 = indulgence, coveting, 망 = hope, desire, 구 = need, needy, 열 = heat, fervor, 정 = emotion, affection)