Emoticons and Smilies in IPB
Emoticons are symbols that use computer characters to convey emotion or tone in an electronic message. IPB gives you the ability to pre-define them in the admin control panel:

Just select the ones you would like to be used in your forum and click on "Update Emoticons":

Avatars in Invision Power Board
An avatar is a graphical image of a user intended to make the network environment closer to reality. Avatars and photos' characteristics can be set from the admincp -> Tools & Settings tab -> User profiles

The default settings should do fine for most of the forums but if you would like to personalize them you can do it in the User profiles section:

It allows to set permissions for image file extensions, Hot-linking (Allow users to use remote URL avatars) which is not a very good idea as some web site have this disabled and hot-linking directly to them will result in inability to display the image, maximum image size, etc.
Inserting emoticons can be done when posting to an existing topics or opening a new one. Once configured, the option will show the available faces (emoticon) in the user panel:

Once logged in you can change your Avatar settings from "Edit Avatar Settings" on the main screen:
