How to connect my iphone to my iCloud account?

Do I have to sync my phone to my laptop? When I log into my iCloud account I can see my calendar events have saved on there but I can't view my photos. In my phone settings I've turned it on so my photos go on there but People keep telling me I need to connect it to my laptop?

If you get a login error when connecting to iCloud, login on this webpage:
http://me.com/move

If it still does not work, it means that Apple servers failed to check your password.
You can change your password on this page to workaround this issue:
Connect to
https://appleid.apple.com/....apple.com.
Choose "Reset your password"
Follow the instructions.
Then, your iCloud account should work fine.