"Totalitarian" typically refers to a state or society in which there is a high level of centralized governmental power, including but not necessarily limited to a lack of what is conventionally understood as "democratic" principles, heavy-handed enforcement of laws and regulations, hyper-nationalistic and militaristic agendas, and complete disregard or disdain for personal security and secrecy. What's funny about this, though, is that it's all about perspective; by these definitions, "totalitarian" could describe far more governments than you might believe.
The problem with the term "totalitarian" is that describes methods, not beliefs, and not whom the methods are targeting. As mentioned above, it essentially describes a state that has a strong, invasive government; but it doesn't describe who the government is being invasive toward, nor does it describe why.
For example, I think we could all strongly agree that Soviet Union-esque socialism, with its emphasis on integration of the state, economy, and the whole of the masses, is quite different from Nazi Germany, which still retained and defended private enterprise and corporations and actively jailed and executed communists and socialists. But because both countries repressed political dissidents and had strong single-party governments, they are arbitrarily equated as being "totalitarian", despite having completely different viewpoints and beliefs, and hating each other like snakes and mongeese.
In a sense, most governments in the world are totalitarian in one way or another. History has shown us governments of left-wing and right-wing origin that have repressed certain demographics in their country for one reason or another, but to compare them, I think, is a mistake, because in order to truly analyze a regime you must not only analyze what it does, but who it does it to, and why it does it, which is why "totalitarian" seems an arbitrary word to me, a buzzword, describing what someone fears will happen eventually rather than describing concrete political praxis.
To cut all of that short: "totalitarianism" isn't inherently liberal/left-wing or conservative/right-wing, because it's an abstract and arbitrarily-defined term that, under the right circumstances, could apply to many governments.
Most totilitatian regimes rose from situations where the former power is in turmoil and the people are willing to trust the dictator for a small hope of recuperation. For example, nazi Germany rose from a devastated post world war 1 Germany, which had suffered major infastructual damage from the war and had its economy in tatters due to economic sanctions and the costs from fighting the war. Hitler promised stability, and a return to prosperity, and the people put their trust in him.