Yes, those green balls are seeds. They turn golden brown when ripen. Your plant is spent, yes. Time to sow new seeds if you would like more fresh leaves.

Here is a link that might be useful: Cilantro seeds

FYI the seeds of cilantro are also a useful cooking spice = coriander.
-bonnie

I concur, those little balls are the seeds. I'm not sure how it would work in your zone, but here in zone 5, cilantro is an extremely prolific re-seeder! I planted one cilantro seedling last year, allowed it to flower and go to seed, and to my great surprise those seeds began sprouting within weeks of falling off the plant and hitting soil! I had a second crop of tender leaves to use in my kitchen, and all in one growing season!

This year, I got a bumper crop of cilantro without planting any new seedlings! I had volunteer cilantro babies coming up everywhere! I expect to see new seedlings sprout soon just from the plants I let seed out this year, and I'm sure to be pulling out more volunteer plants next year!

I would almost use the word "invasive" to describe cilantro. At least, that's how it's behaving in my garden! I love its flavor, and the extra seedlings are easy enough to pull out... and that's my experience with cilantro and its many, many seeds!