What are the boundary conditions simply? I don't know what are actually boundary conditions for incompressible fluids (I don't really understand what they are.)
So may you give me a simple explanation in the incompressible fluids only?
 A: There are boundary conditions for different fluid flow situations and having an incompressible fluid just makes the situation more simple. Note that the flow must be laminar and not turbulent to have an analytical solution.
For example a simple task would be to calculate the flow profile of a fluid in between two infinite plates, when the other (lets say top plate) is moving with velocity V. Looks like this:

(source: reading.ac.uk)
To answer your question: the boundary condition in this example case are that the speed of the fluid right by the lower plate is zero and another boundary condition is that the speed of the fluid right by the top plate is the given V. These come from a common fluid-dynamics rule called the no-slip-condition which you should note to have assumed when stating these kind of boundary conditions. No-slip basically means that the fluid particle that is in direct contact with a solid (being the molecule that touches solid) is held by that solid by friction.
There are of course other kinds of boundary conditions than the stated example, but my guess is that this is the most common among fluid-dynamics.
Firstly this is a very simple exercise and usually given in the beginning in some fluid-dynamics related courses. Assuming from your question you might be in a similar situation perhaps not with the exact case. Without realizing/deducing what these boundary conditions are the task would be quite hard.
Edit: For further reading a quick google search lead me to this course material that goes first through simple laminar flows with analytical answers and then goes beyond: http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/course-textbook/ch4.pdf
Edit2: If you're still puzzled then here is an example of how to solve the question I stated above: https://ceprofs.civil.tamu.edu/ssocolofsky/ocen678/Downloads/Lectures/Couette.PDF.
To explain a little of the steps taken in this derivation (steps you can also follow in any of the problems with different conditions and geometries) once you understand the handwriting:

*

*Stating the deductions and boundary conditions of the situation.

*Using these insights to eliminate terms and simplify the Navier-Stokes equations.

*Solving whatever quantities and profiles from the simplified Navier-Stokes.

