I have heard from many friends that grammatically "reblog" is not a word.
It's something similar to "retweet" from Twitter terminology but Tumblr use it quite frequently.
Wiktionary has it:
And the Urban Dictionary has another definition, which is mostly downvoted (2 up, 5 down):
Basically, even if most people wouldn't recognize it, it's technically a word as long as someone uses it to communicate an idea. By definition, as well as grammatically, it is a word. Some people add to the definition to say that it must be widely used in order to be really recognized as a word, but in that case, the issue boils down to recognition and usage, not the word's status as a "word". As to recognition, I think this one isn't too hard to figure out from context, even when one has never heard it before; as to usage, it is uncommon, but all words start out that way. Blog itself was such a word once.
I haven't found the term reblog in any accepted dictionary, but it is available in the Urban Dictionary. Ultimately, it comes down to how you define a word. Personally, I consider something a word if it's in widespread use and serves a function, especially one for which there is no similar word.
According to Urban Dictionary, reblog has the following fairly obvious meaning:
In conclusion, you can choose to use this word, to express this idea, or not. But this is how new words are created in English; there is no central language authority as there is for French or other languages.
EDIT: Additionally, take the definition with a grain of salt. As evidenced by the two answers to this question, there is no precise definition for many new words. While they are similar, they are not alike. Be careful to use discretion and context to ascertain exactly what someone is trying to say.
Whether some string of characters is or isn't a word is fairly fluid. I don't find revaporize or retransition or undecorate in my dictionary, but I bet most people would immediately grasp their respective meanings. If reblog is in use, it should be considered a word for most purposes.
Obviously, there are some exceptions. If you're playing Scrabble, the meaning of word itself may be understood to be limited to those words found on the official Scrabble word list, or in some agreed-upon dictionary. If you're using a language for which there's an accepted language regulator, newly-coined words may not be officially recognized as part of the language.