Storage on iCloud doesn't replace storage on the phone. iCloud Photos is a copy of the iPhone's Photos Library. The primary purpose of iCloud Photos is to make the same bunch of pictures available on all the connected devices. This means that you can't think of iCloud Photos as a backup service, since it backs up mistakes, and there's no way to undo them. Whatever you do with Photos on your device-- it happens everywhere else.
How much storage space on your phone is free? You should keep at least 10% if your phone's storage free so that there is room to operate on the files. If the phone's storage is nearly full, you may not even be able to delete pictures!
Another use of iCloud is Optimize Storage. You can set this on any device, independent of the others. If you set a device to "Optimize Storage," then Photos may store only smaller images on the device and rely on iCloud to keep the full sized images. Having screen-sized images stored locally allows you to quickly scan through you pictures while saving lots of storage space. And, if Optimize is chosen, and you want to Edit a picture, Photos will reach out to iCloud to get a full sized image for you to work on. Your optimized Library may take up less than 20% of the space of a fully downloaded Library. But an optimized Library may be kept larger than that if the extra storage space is not needed.
Beware, though: backing up a Photos Library with Optimize Storage only backs up smaller images. If you want to keep a true backup on an external disk for safe keeping, then you have to copy pictures from iCloud.com rather than from your phone.
