What is the significance of putting the title="" attribute into the <a> tag?
Because the "alt=" tag only works for images. This aids text-readers for the visually impaired.
Using title="" does the same thing for non-image elements like <h> tags, anchors, anything that needs a little additional description.
Supposedly, the alt="" and the title="" are parsed by spiders and search-engines, but treated quite differently most of the time. Whereas a <h1> tag's text is treated with high relevance, any title="" inside of the header-tag is noticed, but it is viewed with minor importance, probably because it is misused or not very helpful. -Have you ever seen a title="click here to go to the next page" in a web page's code? Although it helps the visualy-impaired, it contributes virtually nothing of any use to the search engine's indexing of that page...
Used properly, alt="" and title="" are both of great value for SEO ("Seach Engine Optimization") and can greatly increase your web page's ranking when someone does a 'search'.