At this time of year the cyclamen are going into dormancy and the leaves are dying off. Reduce water but don't dry out completely.
What you are asking about are the seed heads of the cyclamen. The flowers were pollinated and when the flowers died off the flower stalk retracted into this spring like feature and the balls are the developing seedheads. Come August time the heads will be ripe. The springs will push out again and the seed heads open up to reveal a lot of sticky seeds. These can be sown straight away and will give new corms ready to flower in a few years time. Give it a go and give some seed, you have a lot, to friends to try.

Looking at that picture again I think that the plant is outdoors rather than being a house plant cyclamen: in which case it will be Cyclamen hederifolium flowers from August to October time.
Forget what I said about watering, it does not apply. Only collect the amount of seed that you need to expeiment with and leave the others on the plant.The ants will come for the sugary coated seeds and deposite them around the garden where they may grow for you.

Gosh Bulba can you tell our ants to do that please.....

Theory, Stera, theory. I do find hederifolium plants popping up in our garden, which is wonderful. I no longer try to propagate them myself.

Haha. You are fortunate Bulba - I wish they did here, though they spread nicely where they are.

Thank you very much for the info Bulba, I will look forward to having lots more pretty cyclamen in the garden.
Thanks again.