A deprecated tag is one that is being phased out and at some future point will no longer work on new browsers. You are encouraged to avoid using deprecated tags. You should use either newer tags that...
<applet> <basefont /> <center> <dir> <isindex> <menu> <s> <strike> <xmp>
The transitional document type allows the used of deprecated tags.
An opening tag is what shows the HTML that it is starting there, a closing tag shows when to stop whatever the opening tag said.
It is an acronym for several things, see the link below.