jabber.el supports viewing and publishing avatars according to XEP-0153, vCard-Based Avatars. By default, if you have an avatar in your vCard (see Personal information), it will be published for others to see, and if other people publish their avatars, they will be displayed in the roster buffer and in the header line of chat buffers, if your Emacs can display images. Otherwise, jabber.el will not fetch avatars at all.
To disable retrieval of other people's avatars, set
jabber-vcard-avatars-retrieve to nil. To disable publishing of
your own avatar, set
jabber-vcard-avatars-publish to nil. To
disable avatars in chat buffer header lines, set
jabber-chat-buffer-show-avatar to nil.
There are a number of restrictions on avatar images in the specification. Most of them are not enforced by jabber.el.
Avatars are cached in the directory specified by
jabber-avatar-cache-directory, by default
~/.jabber-avatars/. The cache is never cleaned, so you might
want to do that yourself from time to time.