Skype for the iPhone and iPod Touch has changed the way you can use these devices. It offers some of the features available on the desktop app, but defintiely lacks some features too.
Contacts:
The app allows you to browse through your contact list on the Skype client as well as browse thorugh the contacts list available on your mobile device. Which means you can make a call to a contact who exists on your contacts list on the mobile device but not on the Skype contacts list. The contacts list also allows you to see all contacts who are online and offline, just as in the desktop version.
Calls & Messages Info:
You can get all the call info that you usually get on the Skype desktop application, such as recently made calls, chats, missed calls,chats etc. Although you will not be able to view messages as when they come in using the application tag feature which is present in apps like Mail which show you the number the unread messages. The list will however update on your next login. You can receive only one call at any given time, which sort of sucks but you've got to live with it.
Making & Receiving calls:
You can use the Skype client on your mobile device to make calls only when your connected to wi-fi network. I guess this makes sense, since Apple would not allow them to step on the income of the telephone service provider. Although you can still use chat on the app no matter how you are connected. Also remember that receiving calls is only possible when you're logged into the client (since background processing is not allowed as of now by Apple). You can receive calls from other phones if you subscribe to Skype's Skype-in feature which gives you a phone number. Also you can make calls to other phones if you subscribe to Skype-out feature.
Video calls:
The app does not offer you the ablitiy to make video calls, which the desktop client does. I believe this inconvenience in based on the limitations of the current hardware or firmware but the feature should be possible in the next iteration of the iPhone, which might support video!
Profile info:
You can edit your profile information on the skype client, like switching your profile photography with a new one taken from your iPhone and adding mood messages.