What do those different symbols on achievements mean?

means that the achievement has 6 rewards for completeing its various stages.

Is the collapsed/expanded state of the achievement. If this icon is absent, the achievement cannot be expanded.

means that this achievement is worth 10 points.

Achievement "Points" are an arbitrary number by which you can measure your awesomeness. Nearly all achievements are worth 10 points, regardless of their difficulty.

The one notable exception to this rule is "meta-achievements", the criteria for which are to complete a group of other achievements that are typically related to one another. These are usually worth more than 10 points.