Your inputs here are forwarded to a PHP script, which then processes them and plots them with GnuPlot. This program is free and can do a lot more than we will use in this class, so check it out if you're interested
Other plotting programs commonly used by physicists include Microcal Origin (powerful but expensive), Microsoft Excel (not the best, but on most computers), and Google Sheets (like Excel that can be used online with multiple people, but less powerful/useful than Excel). There are also freeware "workalike" versions of the Microsoft Office package, such as OpenOffice and LibreOffice, although these often lack some functionalities.
When the computer makes a fit it is using a technique called linear regression using a Vertical Least Squares approach. The computer finds the line where the sum of the squares of the differences between the line and the data points is the smallest and calls this the line of best fit.
A better approach, statistically speaking, is to minimize a χ² value, which is the sum of (difference between line and data point)/(vertical error bar on data point) squared - you normalize by the uncertainties. This is especially important if some data has much larger error bars than others. However, this additional level of detail is forgone by most simple fitting utilities, and so we do not use it in this class.