известно means "it is known" and is quite commonly used.
Note that "it" in "it is known" is pretty much meaningless - it's like "it is cold" - and has no corresponding word in Russian, but the "it" in "it means" actually refers to something concrete hence 'Это'.
(Also: значить - "to mean, to signify" is not the same verb as "знать" - to know. )
домой is an adverb, and indicates motion towards home (i.e., homeward, towards home).
дом is in the nominative and merely means "home" - as it would appear in the subject position in a sentence (e.g., дом здесь, "A home is here.")
Дома, like домой, is an adverb and means "at home".
If you want to emphasize walking (in most cases you won't), you will want to use the combination идти пешком. For example:
- Я иду домой пешком = I am walking home.
In regards to the general use of идти: there is a nuance here which is context-related: When you say "Я иду домой" (I am going home), like in English it can mean that you're in the process of going home, or that you're going to start going home right away (a note on that later).
If it's the former, then Russian "я иду домой" usually means walking. It doesn't have to, but this is usually the intention. For example:
- "Где ты? —Я иду домой" = Where are you? I am on my way home (can imply walking)
If it's the latter, the verb идти implies nothing at all:
- "Мне пора, я иду домой" = It's time for me, I am going home
Note: The verb пойти is often more appropriate in this context, i.e. "Мне пора, я пошёл домой". It still doesn't imply any specific mode of transport.
Back to the original sentence: "Это значит, что мы идём домой" is the latter case in most practical contexts. In the rare case that it would be the former, for example:
- "Видишь, что мы не в обмундировании? Это значит, что мы идём домой" = Do you see that we're not in uniform? It means we're going [on our way] home.
it could imply walking, but that's really circumstance-dependent.
Sorry, Duolingo should accept 'walking. "Motion" verbs in Russian are very specific. ходить/идтй means to go on foot. You can not use these verbs correctly if you are using a means of transportation. The latter (идтй) means to go on foot in one direction; the former means to go and return on foot.
Dear avichaim Your phrase translates as "this means we are going home." что is the word "that" as in "this means that we are going home." Although we sometimes state English sentences in speaking without the "that" the word "that" is understood in English if omitted.. Including что makes a grammatically complete Russian sentence.