Why did Russia block the recent U.N. Security Council resolution on a ceasefire in Aleppo?
There were two projects denied in Security Council. Let's discuss both of them.
First, the French project was essentially about (a) ceasefire in Aleppo, plus (b) stopping air bombing especially. It's easy to understand that although (a) is hard to implement (because there are too many armed groups in Aleppo), but (b) is easy.
So if the French project had been accepted then the battle in Aleppo would have become more or less positional fights without any significant advance. And that is a great loss for an attacking side, because they need far more troops to keep the siege than it takes for defenders to break it.
And what is more important, any failure to implement this resolution could be blamed on Russia, as it would be practically only Russia's due to follow it (you have no way to punish An-Nusra for breaking truce).
Next, the Russian project was (a) reviving the Russia-USA September plan about separation between FSA and An-Nusra in Aleppo, and (b) De Mistura's proposal about UN supported humanitarian corridors. That one was denied by USA, UK, France and a few others members.
The item (a) was effectively abandoned by the USA earlier: was it due to their unwillingness or inability, it doesn't matter anymore. It only matters that the USA would certainly fail to implement this item. And (b) is both hard to implement and requires international cooperation, so any future difficulties could be blamed on all sides.
So if the Russian project had been accepted then most of the future problems could have been laid on the USA.
To summarize: (a) no ceasefire in Aleppo is practically possible, and both sides know it pretty well; (b) USA's aim is to make Russia responsible for that, while Russia wants exactly the opposite.
Actually it's a typical sample of the Security Council's work.
Among those have veto power, there are two sides on the Syria issue: Russia+ China and US+UK+France. Each side want to limit the other by any means possible; Including UN resolutions. So Russia veto other sides resolution and want to implement its own plan. But in the media they can not say "we play a game on people life", so each side says we do this because of ... (you know this part; i.e. fighting terrorism, helping civilians, ...)
The point is that using veto power isn't without cost, because the other side can use media to convinced the public opinion against using veto. (So although russia has said that they would veto the resolution, the rival presented it).
So why Russia pay the cost here?
The resolution limits Russia and Assad. The main weapon-priority of Assad against opposition (Daesh, Al-Nusra, Free Syrian Army,...) is Air Force. Also Iran (Russia's regional ally on the issue) claims that US and its allies want to prevent Assad's victory at Aleppo and save terrorists. Russia accepts this viewpoint. Aleppo is a key in the Syria battle.