Mechanical Design refers to the design of all non-organic elements, including but not limited to giant robots, planes, cars, weapons, buildings, streetlights, telephones, and even beer cans! Yes, everything down to the most miniscule object is painstakingly rendered as accurately and with the most obscure detail as possible.
Anime designs are often based on real world designs and often even branded with real world logos like the motorcycle from Akira pictured above. Even fantasy designs like the beautiful Macross VF-1 Strike Valkyrie also pictured above was based on a F-14 Tomcat. This dedication to realism helps to connect the anime to the real world and is a testimony to the otaku nature of the animators themselves. In fact, many of the most famous mechanical designers were engineers in college, before pursuing careers in the anime industry!
Also, a major influence in anime design is Hollywood, specifically the design work of Syd Mead, a futurist and designer whose work on films like Blade Runner and Aliens inspired many anime creators as seen in Bubble Gum Crisis and Akira. Syd Mead is so highly regarded that he has done design work for Gundam and Yamato, two of the most famous and highly regarded Science-Fiction anime series.