This one-liner defines a shell function named fac that computes the factorial of a positive integer. Once this function has been defined (you can put it in your .bashrc), you can use it as follows:

$ fac 10
3628800

Let's break the function down. Assume that we want to compute the factorial of 4. First, it echo's 1, so that the factorial of 0 works correctly (because seq 0 outputs nothing). Then, seq is used to generate a list of numbers:

$ echo 1; seq 4
1
1
2
3
4

We want to combine these numbers into a multiplication expression 1*1*2*3*4. In other words, we want to paste these lines together with a * in between. We can do this using the paste command. To pass the output of both the echo and seq, we group the commands together using the { ...; } syntax:

$ { echo 1; seq 4; } | paste -s -d\*
1*1*2*3*4

Finally, we pass this expression to bc to actually compute it:

$ { echo 1; seq 4; } | paste -s -d\* | bc
24

The $1 in the function means "the first argument", making the function usable with any positive integer parameter.