I've seen the captions described as a dialect, patois, "kitty pidgin" and language play which is well and good but doesn't get to the key visual aspect (silly/cute/adorable cats). Wikipedia offers image macro, a term with hazy etymology but looks like the best candidate at this point. I suppose one could just call it an internet meme but that lumps it in with a vast number of other things that are less well-known.
"Lolcat is an example of __."
Lolcat is an example of anthropomorphisation, internet meme and web humour.
It is also known as a cat macro, or more generally, along with other forms such as the ORLY owl's owl macro, an image macro.
The only image macro definition on Urban Dictionary is from way back in 2005:
Cat macro is a bit later:
A macro is originally a computing term as a single instruction that could expand automatically into several instructions, like a shortcut to save the programmer effort.
The Something Awful forum allowed their users to type in pre-defined words in square brackets, and the software would automatically expand it to show a certain image. For example, typing the [img-timeline] shortcut would show a Timeline of History image in the posted message. [img-hooray] and [img-blownaway] would show early examples of more familiar-looking images:
An old version of the Something Awful FAQ lists some other image macros:
And gives more background information:
Many of these are images with big text captions overlaid, very similar to lolcat images, and the term was then used more generally for any such joke image.
Lolcat, the "language", is also known as lolspeak or kitty pidgin, and is related to leetspeak. For much, much more on the relations and growth between these things, see A Special In-Depth Analysis by David McRaney – L337 Katz0rz.
"Captioned image" is a little less abstract, but i think "lolcat" is the best term.
go with ersatz language (as mentioned by Cameron in the comments) if you are trying to categorize lolcatz as a feature of language.
however, if you are just looking for something general to categorize lolcatz as, try pop culture. as in "A lolcat is an example of pop culture"