AstroCartography involves taking your natal details in terms of date and time but altering the place. The effect is to change the house positions of the planets and also your Ascendant and Midheaven. The planets relative positions do not change, so any aspects in your natal chart will still be there in the relocated chart (chart for new place).
Why do this? Two main reasons, firstly you might be considering moving to a specific destination and want to have some idea of how the move will affect you Astrologically.
The second reason is that you might have some feature of your natal chart which you see as a problem and want to reduce the effect - or a feature that you see as too weak and want to strengthen it. I have Saturn in the twelfth, just short of the Ascendant and in Leo, it's detriment. Now there's nothing I can do about Saturn in Leo but by relocating I could come up with a chart which has Saturn less strongly placed. So I look for a location where the chart would give me Saturn in say, the third - I now might have problems with siblings, but as I've moved miles away from them that's not a worry.
I might want to be a successful writer - Mercury on the MC might help this, so I look around to find a place where Mercury would be on the MC at my date and time (allowing for time zone changes) of birth.
Now that would be a really awkward process, like trying to find the proverbial needle in a haystack. Luckily there is software that will do this for me by tracing the position of Mercury in relation to the world at this time. I can thus find where Mercury is at any location in the world at the time of my birth. There will be several that meet the criterion of Mercury on the MC.
I could look for places where Venus is on the cusp of the seventh or fifth (to improve my chances of love and romance) or if I fancy a highly competitive career, Mars on the MC.
There is a downside of this though. I might find the place where I will have a good chance of being a successful writer but if Mercury has bad aspects to other planets it might still not come to pass. Even if it does, I might have improved my chart in one direction but find it's worsened in another - moving Uranus into the Seventh and increasing my chances of a divorce - I spend so much time writing my wife leaves me.
It's virtually impossible to improve one thing in the chart without making something else worse. Some people may still go for this move and accept the cost.
If you've had a chart done, the chances are you've got a map of the world with some wavy lines on it and also some vertical lines for it. Each line represents a planet and it's position in the chart - Such as Mars on the Ascendant or Neptune on the MC. These give you the places where the desired characteristic occurs - you then choose which one you fancy. Some places may meet your desired planetary placement but be unsuitable - they lie in the middle of the Pacific Ocean, or in the Sahara Desert or in Iraq. So the choices will be reduced and indeed you might prefer to live where you are now than in the possible choices available to you. There are other reasons for choosing a place to live than Astrology. If I wanted Mercury on the MC, I have to move to Alaska - I think, I'd rather stay where I am! (Sorry to members in Alaska
)
Of course this also depends on the theory that relocating will lead to some parts of your chart 'improving' and therefore affecting your life It's not a universally accepted view.