In the context of your example, the speaker is saying:
* "I dig this hospital jive." This means they understand and appreciate the atmosphere or "vibe" of the hospital.
* "Them nurses understandable." This means they find the nurses easy to understand or relate to.
* "Nice but understand..." This suggests the nurses are not only friendly and pleasant, but also competent and capable.
The phrase "jive" in this context comes from the jazz and African-American culture of the time, and it carried a sense of being in the know, or understanding the unspoken rules and trends of a particular group or scene.
So, the speaker is saying that they like the hospital's atmosphere, and appreciate the nurses' skills and personalities.