The common understanding of what's left and what's right is the European one. Leftists are expected to be tending to liberalism, dovish and support welfare-state/socialism while rightists are expected to be tending to religion/tradition or conservatism, hawkish and capitalism.
Well... sorry to be the one to tell you this: the world is a bit more complicated.
The 20th century exhibited leftists who were terrorists more than liberals, rightist who were more populists than capitalists, as well as other numerous variations.
So, when we will be discussing the left and right in a certain realm or country, it must be understood in its respective context. If you'd like us to elaborate on something, please post a comment under the related post.
In the context of our previous post, when the government in Israel is trying to denounce something or someone as leftist, it means to point out dovish ideas mainly in the context of the Israeli-Arab conflict.
The Israeli left is commonly correlated with its affluent middle class and old elites holding social-democrat views, while the right is correlated with the popular and conservative masses and religious public. Leftist economical ideas were set aside by both right and left main parties while small parties in both left and right hold fractions of leftist economical ideas.
Argentine, is a different example. There are 2 main parties. One which would be a classical European left party, liberal-social democrat, but it is tainted as an upper-middle class only bastion. On the other hand, there is a populist party which has factions which brutally privatized the whole country when they ruled and other factions which are anti-American, anti-capitalist and affiliated to the left side of the South American political map (Chavez, Castro, etc.)
There are many other examples, but that's enough to illustrate our point.