In the Admin CP, you can create Custom User Fields.
So if you wanted a field to show during registration that asked someone's eye colour:
Go to Admin CP > Users > Custom User Fields > Create New Field
Then fill it in. There's lots of different choices.
Basic options for the title, description and ID. Where you want the option displayed. The type of field.
Here you can set options such as if it's required, whether you want it showed during registration. Even if you want it viewable in the profile pages, editable or in the message user info.
There's loads more stuff you can do, but those two pages are what you want for what you've asked for.