Maxima is a Computer Algebra System (CAS) it is two complex to be fully described here, see the inbuilt Help file. Below I have described the Czimps interface to Maxima.

You can use Maxima manually by editing a Maths String, or by Running a MaximaCommand Function, you will find this function on the B menu.

When you first edit a Maths String it will look like the above.

After the first time you press OK without the last line being blank you may have to wait while Maxima is initialized, then the Edit dialog will change to the above.

Finally if you press OK again the Maxima notice will disappear and you can type more commands.

If you Run a MaximaCommand Function you have the option of capturing the result in a String. Also if Maxima draws a graph this will be automatically captured as a Czimps Image.