When I think about walls, these are the three main questions I think of:
1. What are walls?Wall is just that - a wall. If nothing else happens, it will likely become one side of a possibly large territory. So, to prevent this, the opponent will always have to worry about it. This is a good thing.
Another aspect of the wall is strength - although these two ideas are not really the same. Strength allows you to fight in other parts of the board without worrying about the wall/strength coming under attack (as in - splitting attack). This gives you some peace of mind, which is good.
One important thing to note here is that walls and strength are not the same. Some walls can be week, some can be very week. Such walls have much more limited use because you *do* have to worry about them getting under attack and you cannot afford to play freely without worry. So it is important to judge the strength of your wall as well.
But all in all - a wall is a good thing for you and potential trouble for your opponent.
2. How to play with respect to walls?To me, Go groups (or even stones) are like magnets - except that they all have the same polarity and so repel each other. Generally, the larger a group of stones the more its repelling force - thus you play farther away from it. This goes both for your own groups and for the opponent's groups. Walls are groups wich repel the most (because all the repelling force of all stones is pointed in the same direction), usually, so you try to play away from them.
Of course, as the game progresses, you play closer and closer to other stones/groups. So I think about it as the magnetic 'power' of the stones diminishes over time. Eventually, a moment will come when you be able (or have to) to play close(r) to a wall, be it your wall of your opponent's. The trick is to utilize your own wall before that happens, and prevent your opponent from utilizing his/her.
You can utilize your own walls by trying to play stones which work with the wall, outlining areas or even moyos. This will force your opponent to jump in, hopefully, at which point you can attack. If he/she fails to invade or reduce, the wall will turn directly into points eventually.
Conversely, you will try to prevent your opponent from doing the same to you.
3. How to use a wall?I already hinted at most of it - you use it for attacking, for peace of mind (fighting elsewhere without worry), and for building territory/moyos.
Most popular way of using a wall is for attack. This combines the concepts above. Because your opponent has to worry that, if nothing is done, the wall will eventually become a side of a large territory, at some point he/she will have to do something about it. This means approaching the wall to minimize its potential. In such situation, the approaching sone can be pincered and might come under attack. The main idea is to push the weak stone towards your wall.
A typical outcome of such fight is not usually death of a group, but maybe another wall, facing in some more advantageous for you direction. You can imagine a series of walls, each created by attacking stones approaching the previous wall, with the last wall eventually being used to make direct points. But sometimes the attacking groups die... or other groups die when you can stage a splitting attack. This all connects to the reasons for attacking and the advantages you can have by doing so - but this is another topic.
Another thing is - there is also a danger that during the course of the game, a wall will become neutralized. This can happen, for example, if your opponent will build his/her own wall facing your wall, or create a strong group in vicinity of your wall. A lot of times this involves such concepts as proper joseki choice or even non-joseki moves. It gets complicated.
And also: Influence?I was trying to explain how I see walls without using the word 'influence', because this is what everybody else seems to be doing.
But influence is a great way to explain many things in Go, which is why people keep talking about it so much. You can see stones/groups/walls as radiating influence. The concept of neutralizing a wall can be then explained by overlapping spheres influence. If influence is not deal with timely, it might easily become solid points. And so on... Walls create more influence than other kinds groups, so this is one reason they are important to understand.
PS>
Not sure if all this makes any sense... cannot think straight today... just another day at the Bantari office.
