I've heard the words of my headline tossed around the garden this spring, figuring they meant something but not getting the concepts entirely. But I think I have it now, and it's worth sharing. (Or so I think; you decide.)
The times I've heard the terms tossed, the subject was tomatoes. According to this tomato-growing site, determinant varieties, including the well-known Roma variety, grow to a roughly defined height, stop growing when the fruit sets at the end of each branch, ripen about the same time, and then die.
Indeterminants keep growing until frost — flowering, setting fruit, and ripening all at the same time, on different stalks.
Recently, my gardening mate Michael Smith, who horticultures for a living, shared a brief film on pinching out young tomato-plant branches that I later realized are what others call "suckers," another term I'd heard but didn't quite grasp. (There's a lot of that for me in the presence of actual gardeners.)
After watching, I went out into my own garden and pinched — or clipped — all the suckers, which are identified as growths emanating from the juncture of the main stem and a side shoot. The reasoning, as I understand it, is that these suckers will make the plants bushier, bringing no advantage, at the expense of energy that would better be applied to the fruit.
Then I noticed that my eggplant plants also have suckers, and wondered if I should cut them out, too. Luckily, I didn't. I asked around among the gardeners and got no definitive answer, though one guy said he thought it made sense, and another observed that both tomatoes and eggplants are from the nightshade family.
Turns out, according to a consensus of websites I found, though none authoritative enough that I'd link to, that eggplants are determinant, so every branch I cut off would just be limiting yield, instead of concentrating energy in the "right" places.
There still remains the question of whether all eight of my tomato plants are indeterminants. That's something I ought to know, but don't.