To tell the gate that you are done dialing.
To dial within the current galaxy, there were 6 symbols for spacial
coordinates, ending with a point of origin.
To dial to another galaxy, 6 symbols for spacial coordinates, 1
symbol for the galaxy (like an area code, seemingly), and
terminating with the point of origin.
To dial something else, it's 8 symbols plus the point of origin.
As far as I remember, this has only been seen once - when dialing
Destiny in Stargate Universe.
It can't be automated in the DHD due to the ability to dial manually on Milky Way gates. I would guess it was included on the others to keep the number of symbols consistent.
(Side note, the Tau'ri symbol, the pyramid with one sun, has been seen on at least one gate besides the one on Earth. Season 2 or 3, I think it was... So the points of origin aren't unique to each gate. Based on the original description of the coordinate system, most likely the Tau'ri symbol is part of a constellation that our sun is actually in, that's only visible from some other planets.)
So, just to add, the comments on the other question/answer reminded me of some things. From the comments, after I suggested the above without expanding on it, this was this response: (And it also came up in this answer's comments as well)
That would make sense, but there's no reason the button couldn't pop
on the terminating "character" for the PoO as well. Certainly it'd be
a better user experience... it would require the Gate to let the DHD
know what the appropriate character is, but we know there's two-way
communication (status/error codes etc) anyway.
No, it wouldn't make a better "user experience", it would introduce an inconsistency. The Milky Way gates were specifically designed to be able to manually dial in addition to using a DHD. If the DHD popped on the point of origin, you now have an extra indirection: 6 symbols if there's a DHD, then in the rare chance there's no DHD and you have to dial manually, you have to remember that there was also a point of origin.
Including the point of origin every time makes it almost impossible to forget it in those circumstances.
In addition, at the beginning of SG-1 6x09, "Allegiance", we see another use of the Stargate that seems to require a DHD: In a funeral ceremony, the Tok'ra presses the red crystal on the DHD without entering an address. The unstable vortex forms to destroy the body, then immediately deactivates. Given the above, this seems to be further evidence that the DHD termination character (^D, red crystal) does not have the same function as the Stargate termination character (\0, point of origin).