STE(A)M stands for Science, Technology, Engineering, (Arts) and Math. The acronym describes the skills used to identify, solve and evaluate solutions to real world problems to work through the Engineer's Design Process.
The Design Process is a method for working through the steps needed to produce a solution to a problem. It is closely connected to the Scientific Method but is focused on the production of solutions rather than determining the "why" of various phenomenon.
Using Stem in the classroom involves engaging students with using various STEM skills and exposing students to the Design Process. Thinking of STEM in this way allows students to focus on just a few of the manageable aspects of STEM skills or the Design Process at a time.