All-pairs testing or pairwise testing is a combinatorial 
testing method that, for each pair of input parameters to a 
system tests all possible discrete combinations of those 
parameters.

In pairwise testing, two testers combinly working on the 
same system for the same project.
The main aim of pairwise testing is, to exchange of ideas 
between the testers.
The sucess of pairwise testing depends on coordination 
between the testers.

TO conduct the testing senior tester with the help of 
junior tester is called pairwise testing.This much of 
testing is conducting when the time is less for testing

pair testing is one type of ad-hoctesting due to lack of 
domain knowledge junior testers are paired up with the 
senior testers ,called pair testing .

pair wise tsing is an effective test care genertion
technique that is based on  the observation  that most
faults are caused        by interaction of atmost two
factors. pairwise testsuite cover all combinations of two
therefore are much smaller than exhaustive ones yet still
very effective in finding defects.
 
paurwise testing is a adhoc / monkey testing techniques used
in case of lack of time, lack of documentation, lack of
skills, lack of  resources etc.
the lest lead will use this tech due to lack of time . they
will make a tester as a pair with developer. they both cont
testing nd coding parallel.

Due to lack of knowledge senior testing engineers are 
grouped with junior testing engineers to share their 
knowledge.

testing a single programe by one pair is nothing but
pairwise testing(Eg for pair:two testers,1developer and 1
tester,or end user and tester).

Pairwise (a.k.a. all-pairs) testing is an effective test 
case generation technique that is based on the observation 
that most faults are caused by interactions of at most two 
factors. Pairwise-generated test suites cover all 
combinations of two therefore are much smaller than 
exhaustive ones yet still very effective in finding defects.

There are also some automated tools to generate pairwise 
combinations like TestersDesk.com.

Suggested links:
www.TestersDesk.com
http://www.pairwise.org/

Arif and Bhagawati are correct.  

Pairwise testing is the simplest form of combinatorial testing.  Another way to state what Arif and Bhagawati have correctly stated is that a primary goal of pair-wise testing is to achieve 100% coverage of potential dual-mode-faults.  

More sophisticated combinatorial testing methods can also guarantee 100% coverage of all potential triple-mode-faults, 100% coverage of all potential quadruple-mode-faults, etc.

If you are interested in finding out more, a recommended site is CombinatorialTesting.com