The Linpack for Android application is a version created from the original Java version of Linpack created by Jack Dongarra.  That version is located at netlib.org

The LINPACK Benchmarks are a measure of a system’s floating point computing power. Introduced by Jack Dongarra, they measure how fast a computer solves a dense N by N system of linear equations Ax = b, which is a common task in engineering. The solution is obtained by Gaussian elimination with partial pivoting, with 2/3*N3 + 2*N2 floating point operations. The result is reported in Millions of FLoating-point Operations Per Second (MFLOP/s, sometimes simply called FLOPS).

This test is more a reflection of the state of the Android Dalvik Virtual Machine than of the floating point performance of the underlying processor. Software written for an Android device is written using Java code that the Dalvik VM interprets at run time. 

Questions asked about the app:
What is the purpose of this app?
This is a simple benchmark test to show performance relative to other phones for a standard calculation.  Linpack has been used for years on all types of computers, with a version used to rate the TOP500 computers in the world.

What speed is better?
A higher number is better.  From the Top Devices list, you can see that each device has a certain range that they all come in at.  What can effect the number is what else is running on android and the ROM version.  It appears that Android 2.0 will also improve performance.

Does having faster speed improve the android phones or what?
Yes, it should.  The Dalvik VM has a huge impact on the Linpack number.  A better number on the same device would indicate that a new version update has improved performance.  Or it could show that something has gone terribly wrong if the number goes down.

Comments
VoxLuna  5 Jan 2010 
Might serve a purpose, but bland layout (and ugly AdMob).  Why a splash when there’s also a weblink button?  See “Louder Volume” app for UI Inspiration.
Reply:  Great input. I agree with it all.  I will remove the splash in a future release.  I do like the UI recommendation.