What is the purpose of meta tag in html?

metatag was used for caching, meaning storing a web-page locally.
It ensures that secure https pages can't be stored.

for shortly information about webpage , 'identity' of webpage and it's for easy identify for Serac engine Optimation (SEO).
Using meta tags to helping web crawlers index the pages more easily in the search engines, but not all web crawlers or robots meta tag's attention again.
contents in meta tag can also be ignored robot crawler, especially if the words in the meta tags are not included in main web content at all.

META data is machine parsable, making it easier for search engines and other sorts of robots to understand content in your page.

Meta tags speaks with the search engine directly, it has nothing to do with the page formatting in any way...meta tags are used to give information about the page owner, website, sitemap.xml (if you are submitting to google) to know more I suggest you to read an article here.
http://www.webmarketingnow.com/tips/meta-tags-uncovered.html

Meta tags help your site to be indexed by crawlers / search engines.
Each web page has meta tags information.
Meta tags contain keywords related to the page content or website which help your site be indexed and searched.

Hi kamran Hyder, A meta tag is a specific HTML tag used to define meta data on the Web Pages.
meta tag provides information such as: ~ Who has Created the Page ~ How often the Page has been Updated ~ What the Page is all About ~ Which Keywords represent the Page's Content ~ How often the Web Page should get Refresh ~ Appropriate Key Words for Web Crawlers / Searching Engines ~ etc...
There are Dozens or Hundreds of Several meta tags.
All are Optional on the Web Page, although some are Highly Endorsed based on the Company’s Requirements and Industry Standards.
An Example of meta tag is:

A meta tag is an HTML coding that contains metadata such as keywords about a webpage.
Meta tags inform web crawlers about the page.

Meta tags are HTML codes that are inserted into the header on a web page, after the title tag.
In the context of search engine optimization, when people refer to meta tags, they are usually referring to the meta description tag and the meta keywords tag.
The meta description tag and the meta keywords tag are not seen by users.
Instead, these tags main purpose is providing meta document data to user agents, such as search engines.
In addition to the well-known meta description and meta keywords tags, there are other useful meta tags, including the meta http-equiv tag, meta refresh tag, the meta robots tag, the meta copyright tag, and the meta author tag, etc.
These tags are used to give web browsers and search engine spiders directions or data on various information.

Taps make writing the code is more is..............so you can easily notice where the block starts and where it ends but every open tap need the close on unlike XML....

It was very effective before but google algo is changed now and has made drastic changes in SEO techniques and now you have just snippet displayed with search result using these tags.

meta tag is used for browsers as well as search engines.
From the meta tags only your site will be shown in the search results.
If you want to avoid your site from search engine search results, for that also you have to use meta tag.