Sharing files with others using iCloud? From what I know, iCloud is like a personal storage and you uses your own Apple ID for it. Is it possible for users to store for example an image and be shared with other users?

Which means something like DropBox. You upload files into your DropBox account and there will be a url that allows other people to download the file.

Does iCloud has this kind of function?
I don't believe so, no. iCloud is meant to be a cloud-based backing store for apps, not a file-syncing service like Dropbox. It's a subtle difference, but consider that all interactions with your iCloud data happen through apps (Address Book, iCal, iPhoto, iTunes...), rather than with the individual files themselves.

So any sharing functionality for a given type of data will likely be delivered through the associated app(s). Whether it will make use of iCloud directly is uncertain, but although still in early days that doesn't seem to be the current pattern.