1. Hole, door, entrance, gate, slit, vent, opening, issue.
2. To pass through, appear, emerge, come out; to rise, as the sun.
3. To graduate.
4. To say, utter, speak.
5. To gain, win, profit; to draw interest; winnings, gain, profit.
6. Trap, snare.
7. idiom. Almost.
I bet you did not realize that there were so many meanings for the word puka. Puka, second only to pau for frequently used Hawaiian words in daily life (of course I am not counting aloha and mahalo because everyone worldwide uses these words).
If you look at the majority of the translations above you can see that they are related (now is the time for you to stop reading here and glance up and review the meanings again). You need to visualize a hole and things being able to emerge from a hole (I like to visualize a hole, like a blowhole, and water shooting out of it). Visualize the sun coming out of the hole. Visualize a graduate reaching for the stars out of the hole. Visualize what you see emerging from a hole (i.e., words leaving your mouth). Visualize the winnings which will "take you out of the hole". You just have to keep in mind the visual.
There is one way that puka is misused. Sometimes what we think of as a puka is actually a lua, a pit. Take, for example, what we would refer to as a hole in the ground. In English we call it a hole (like a pothole) but in Hawaiian it is not a perforated thing where you can see light at the other end. It is a lua, or a pit of sorts. Much like a toilet. No light at the other end.
Puka mai ka lā i ka hikina - The sun rises in the east (the first line of a mele kaʻi, the mele done when a hālau hula emerges onto the stage)
He puka ko ka lole wāwae - The pants have a hole (puka pants!).
E puka ana ʻo Kaipo i kēia makahiki aʻe - Kaipo is going to graduate next year.
Puka maila ʻoe, ua kala kahiko i Lehua - Now that you have come, [what we had] has long departed to Lehua
See if you can solve this ʻōlelo nane (Hawaiian riddle): Puka kinikini, puka kinikini, ʻaʻohe ona puka e puka aku ai - a multitude of puka, a multitude of puka, but it has no puka to pass through/emerge from.
What is it?