Most webmasters don’t see any difference between image alt text and title mostly keeping them the same. A great discussion over at Google Webmaster Groups provides an exhaustive information on the differences between an image Alt attribute and an image title and standard recommendations of how to use them.
Alt text is meant to be an alternative information source for those people who have chosen to disable images in their browsers and those user agents that are simply unable to “see” the images. It should describe what the image is about and get those visitors interested to see it.
Without an alt text an image will be displayed as an empty icon: 
In Internet Explorer Alt text also pops up when you hover over an image. Last year Google officially confirmed that it mainly focuses on an alt text when trying to understand what an image is about.
Image title (and the element name speaks for itself) should provide additional information and follow the rules of the regular title: it should be relevant, short, catchy and concise (a title “offers advisory information about the element for which it is set“). In FireFox and Opera it pops up when you hover over an image:
So based on the above, we can discuss how to properly handle them:
- the both tags are primarily meant for visitors (though alt text seems more important for crawlers) - so provide explicit information on an image to encourage them to view it or get them interested.
- include your main keywords in both of them but keep them different. Keyword stuffing in Alt text and Title is still keyword stuffing, so keep them relevant and meaningful.
Another good point to take into consideration:
- According to Aaron Wall, alt text is crucially important when used for a sitewide header banner.
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