Picasa asks if "you want to upload and replace all the thumbnail photos from your People Albums to your Google Contacts". If you click on "Upload", Picasa saves the photos to Google Contacts and you can see them in Gmail or in any other application that synchronizes with Google Contacts (for example, Android's Contacts app or iPhone's Contacts app, if you use Google Sync).
If you don't want to upload photos for all your contacts, you can click on one of the people from Picasa's sidebar, right on a photo and select "Set as Google Contacts Thumbnail". You can also enable "Upload people album thumbnails to Google Contacts" from Tools/Options/Name Tags (or Picasa/Preferences/Name Tags on a Mac) to upload the new thumbnails you select in Picasa.
It's strange to see that Google didn't add this option to Picasa Web Albums and that the photos tagged in Picasa Web Albums aren't displayed in Google Contacts. Google could at least offer the option to pick one of the photos tagged in Picasa Web Albums when you add a picture to one of your contacts. Right now, you can only select a photo from your public albums.