The adidas logo symbolically speaks to the purpose of the shoe because the thick lines look symbolic of the sport track and the comforting feeling when the shoe elevates as you run. The thickness in the lines could represent the cushion in the shoe.
The target logo is very self explanatory but very loud. It's actually a target in the center which symbolically means this store is where you can target exactly what you want, and the store has everything to fulfill your needs.
The twitter bird speaks volumes about the social network and its purpose, which is to allow people to express themselves without apology with short sentences and images. The bird looks like it's looking straight up and singing or excessively talking as many twitter users do.
The Jordan logo is powerful because it makes everyone feel like wearing the shoe will make them play and feel like Michael Jordan.
The Puma logo is symbolic of how fast the shoes will make you and how powerful the soles of the shoes are when worn. The image of the puma represents fierce speed!