For the eight chevron, it's used as an additional calculation for extra-galactic travel (outside of our own galaxy), which serves as distance from here to there. For Atlantis, you'd most certainly need it as it is sitting in its own galaxy and separate from our own.
The ninth chevron is less conventional and is mainly used for Destiny as it points to a specific gate instead of a location. Because Destiny does not inhabit a fixed point in space like every other gate we've come across, it can't be dialed without this chevron due to the nature of where Destiny may be at any given time.
Both require a lot of energy to work and create a functioning wormhole for travel, much more than your average Stargate is meant to handle. However the last chevron, no matter how long the address, will be the point-of-origin and is thus not always the seventh chevron. If you were dialing to Atlantis, you'd still need an extra chevron for the extra-galactic address but the last (now eighth) would be the origin gate. The Atlantis chevron is inserted someplace between the address and origin chevrons. Same for the ninth.
For more information, I found the Stargate Wiki to be a great resource as well as where I remembered most of my Stargate-verse. It's been a while since I've been to visit this universe.
EDIT: More information with thanks to Arammil
The Stargate address can be seen as mathematical equation with the solution being the destination Stargate. Thus, if letters A-F were the first sixth chevrons, with the letter P being the point-of-origin (usually Earth), would make an address/equation look like this:
A+B+C+D+E+F+P = Destination
If you added an eighth chevron, to get to Atlantis, you'd add that extra co-ordinate (which we'll name G) for the extra-galactic travel needed. Our address/equation would look like this:
A+B+C+D+E+F+G+P = Destination
You can see that our P value (point-of-origin) has stayed in the same relative, but not absolute, spot as the first: the last value added to create our destination value.
And, finally, for the ninth chevron, our address/equation would be like so, assuming H for the rough equivalent of Destiny:
A+B+C+D+E+F+G+H+P = Destination
Again, P stays in its relative position to the others and remains as the last variable to be added to our destination address. Of course, how the actual "math" of gate travel is not known, and to my knowledge was never adequately explained in the show, so this is the best I could come up with. I'm sure that if they did, it would be a much more complex equation.