L(x,alg) evaluates an algebraic expression and stores it in a variable. So, for example, L(X , Y^2) means "let the solution to Y2 be stored in the variable X" (^ means "to the power of," so Y^2=Y2). The fact that L(x,alg) stores the solution in a variable allows you to pass the result on. To see how L(x,alg) works, try the following:
Press <HP CALC> <MENU> S F4 and you're ready to start entering equations into the Solver Editor. Type in Z=L(X , Y^2). Press <ENTER> and F9. You should see Z and Y in the variable menu. X doesn't show because it's not part of the equation, it's just the variable that the solution to the equation is going to be stored in.
To "coax" X into the variable list, press <ESC> F2 to edit the equation and change it to Z=L(X , Y^2) + 0*X. Press <ENTER> F9. Now you should see X appear in the list.
Note that the equation didn't change by adding 0*X (0*X=0). All we did was put X in the equation somewhere other than the first argument in the Let( ) function.
In other words, if we use a variable only as the first argument in the L(,) function, we won't see it in the Solve Calc variable menu. If we use it elsewhere in the equation, the variable will appear in the menu.
To see L(,) in action, press <Down Arrow> a couple of times to move the highlight bar to the Y variable (Y = 0.00). Key in 4 and press <ENTER>. Now move the highlight bar to Z and press <Space Bar>. The L(,) function evaluates Y^2 and assigns the solution (16.00) to both X and Z.