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This metaphor almost certainly refers to the practice of establishing the first conditional check in a while loop. If you don't do this, the loop won't work.

int i = 0; // prime the pump
while (i < 10)
{
    Console.Write("While statement ");
    // Write the index to the screen.
    Console.WriteLine(i);
    // Increment the variable.
    i++;
}

The primer can be a read statement, or whatever properly sets the initial condition. Setting the initial condition using a read statement is called a "Priming Read."

string line;

using (StreamReader file = new StreamReader("c:\\test.txt"))
{
    line = file.ReadLine(); // Priming read.
    while(line != null)
    {
        Console.WriteLine (line);
        line = file.ReadLine(); // Subsequent reads.   
    }
}

In C#, the two Readline() calls can be combined into a single statement within the conditional, essentially avoiding the primer:

while ((line = r.ReadLine()) != null)
{
    Console.WriteLine (line);
}