Mechanical Engineers create useful things for our world. Everything you see from a rocket to a toothbrush was designed by a mechanical engineer. So in general, mechanical engineers harness the laws of physics to create useful inventions for humanity. Typical areas of study for a mechanical engineering student include Statics, Dynamics, Heat transfer, Thermodynamics, Strength of materials.
If you spent a day with a typical mechanical engineer, you would spend most of your time looking over his shoulder as he created solid models on the computer using CAD software. This is by far the main job function that is done day in and day out. Occasionally, he will be in meetings discussing design decisions, but the majority of his time is spent in front of the computer. I could continue on with a description of mechanical engineering, but as they say a picture is worth a thousand words so here is a great video showing the day to day of a mechanical engineer. It shows the steps from CAD design to the actual manufacturing of the parts. As I said before, the design portion using CAD takes the longest to complete. Once you have made your design choices it just a matter of producing the parts and then assembling them.