The title of the song can translate to "The Grass At Home" or "The Grass Near Home" since the preposition "у" in Russian can mean "at" like the French "chez" or "near" as in "I have 5 bucks on me" near (there are other words in Russian that mean near but I won't ramble on about that)
As for what going on in the song I believe it's about cosmonauts in space who dream of home. One thing about exam time since I haven't made the decision to rent myself a place is that I look forward to is going home. Though I may not be a cosmonaut in space who is many many kilometres far from the Earth I spend most of the year on an island in which there is a 1.5 hour time difference between here and home. Me being in 4th year university I'm already used to being on my own but when the days get closer and closer to coming home for the holidays I do get the homesick feeling. Sure the grass at my home in my hometown may not be green (covered in who knows how many metres of snow by now) and I'd pretty much try to avoid people once I get back I pretty much miss the comfort of not having to worry about waking up early for class and a bed that doesn't feel like foam.
as for a translation of the lyrics, a version can be found in this video
Not sure who comes by here often but anyone have their say on homesickness?