Alan Bleiweiss: They`re not alt "tags". They are alt "attributes" within image tags. In an image tag, you have the href attribute, which necessarily contains the URL pointing to the image itself, and the alternate text attribute (the "alt attribute" which provides visually impaired visitors and visitors who have image display functionality turned off, the ability to read text you provide that describes what the image shows. Because it`s primarily for visually impaired visitor needs, and overall accessibility requirements to provide an alt attribute, doing so requires care and respect for those needs. And when done properly, helps search engine algorithms understand what that image is about as well, and where that can reinforce topical understanding of the page those images are placed on.
Alan Bleiweiss: You can also have a "title" attribute, which can be used by various social media channels - like Pinterest. Just be careful to not go too far in trying to artificially increase SEO by stuffing those attribute fields with keywords.