A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the second) James Clift will explain all of these terms in detail. In his first talk he defined products, pullbacks, general limits, and exponentials and in Part 2 he explains subobject classifiers.
The lecture notes are available here: therisingsea.org/notes/ch2018-lecture4.pdf.
For the general seminar webpage see therisingsea.org/post/seminar-ch/.