NOUN

Mathematics

A condition that is required to be satisfied at all or part of the boundary of a region in which a set of differential conditions is to be solved.

http://www.oxforddictionaries.com/definition/english/boundary-condition

physics: a condition which a quantity that varies throughout a given space or enclosure must fulfill at every point on the boundary of that space esp. when the velocity of a fluid at any point on the wall of a rigid conduit is necessarily parallel to the wall.

http://www.merriam-webster.com/dictionary/boundary%20condition

Corrrection~ Control and Electrical engineering ARE very familiar with initial condition.

It used in to solve some problems in real life like we use it if we want to know the temperature distribution of a bare or heat exchanger's fins or something like that. In this case, we use Fourier series and also they use it in vibration. Also, it used to derive many engineering equations. It is more likely to be like integration. for instant:

at x=0 m  then T= 20C

at x= 100 m then T=100C

Where:

x: indicat position

T: temperature

C: degree Celsius

Sometimes , we need initial condition with it which concern with time, for instance:

At t=0sec then T= 0C

at t= 30 sec then T= 3C

Where:

t: time

sec: second

C: degree Celsius 

However, in Mechanical Engineering we need both of them but Control and Electrical engineering is very familiar with initial condition.

I can give you an example in information science. I am not really sure if that is what you want..nevertheless:

For example you can number a list. The first item in the list mostly has the number 0, and the last item the number (Size of the list minus one). If you run through the list, you refer to the items by their number. Now if you start with number 1, instead of number 0, and you end with the number equal to the size of the list, you address the wrong items. Especially at the bounderies, the borders, this can lead to unwanted behaviour.

It is related to Mathematics/Physics. You can google it for exact definition. I am not aware of it being associated with contract.