A Bongard problem consists of two classes of pictures. Each class is represented by 6 sample pictures. The goal is to find the difference between the two classes, i.e. which aspects of the different pictures are fundamental to characterize each class.
In other words, finding the feature(s) that groups together the pictures inside the two classes but clearly separates between the classes. The property shared inside the classes and that distinguishes between the classes.
For example the solution to BP #04 is:

Pattern recognition is a domain in which humans (and other organisms) excel while computers perform poorly.
Having computers excel at this task is one of the big goals in Artificial Intelligence studies.
Bongard problems (and in general pattern recognition studies) are also relevant in Cognitive Science research. They help understanding the ways we process and identify information, how we interpolate our stimuli....

Harry Foundalis was working at writing a program that would be able to solve BPs. His web pages are a very good source of information on BPs.

The links at the top of the page lead to the 100 original problems by Bongard plus those created subsequently by other people. Foundalis also has a page listing 280 problems.

• Alexandre Linhares - A paper on the ontology of Bongard Problems
• Andreas Ryge - Machine learning techniques applied to Bongard Problems
• Sergii Kharagorgiev - Solving Bongard Problems With Deep Learning
• Pradeep Mutalik - Numberplay: Is Human Intuition Essential to Unraveling Puzzles?
• Pradeep Mutalik - Bongard Problems and Scientific Discovery