It takes quite a bit of life-support equipment to keep fish alive in a glass box. Typical gear includes water pumps, filters and heaters. Depending on your specific aquarium setup, you can hide this equipment in a number of ways.
Many species of fish feel safe in the presence of dense thickets of vegetation. You can use dense aquarium plants to hide water pumps and other pieces of aquarium gear from view. Fake plants work well for this application. Additionally, with plastic or silk aquarium plants, you do not have to worry about current or pump inlets damaging the plants. You can use live plants to hide aquarium equipment. However, keeping thriving aquarium plants is harder than it looks. Many species of aquarium plants require powerful lighting and supplemental carbon dioxide to thrive, and can damage water chemistry if you fail to provide these conditions.
Some species of fish, like African cichlids, prefer rockier environs to vegetated streams. Fortunately, you can also use rocks to hide equipment like water pumps. In most cases, you want to use chemically stable rocks like slate or basalt. In marine tanks and aquariums catering to African cichlids, you can use calcium-bearing rocks to buffer the pH and increase hardness. With rocks, you need to make sure you're not blocking the flow from water pumps or crushing your aquarium equipment. You may need to secure the rocks with aquarium putty to make sure they don't shift and smash your equipment or fish.
Some aquarium equipment, like external pumps and hang-on filters, can sit behind the aquarium. You can easily hide this equipment with an aquarium background. Pet shops sell printed aquarium backgrounds with a variety of themes. If you prefer a simpler background, you can use plain black poster-board. Additionally, some pet shops sell 3-D backgrounds. These are made out of plastic and designed to look like rockwork or woods. These background as designed to go in the aquarium, and can hide pumps and other gear in the aquarium itself.
Sump filters first entered the aquarium hobby as tools for keeping delicate marine organisms healthy but have found their way into the freshwater side of the aquarium hobby. A sump filter -- aka trickle filter or wet-dry filter -- is a separate reservoir of water plumbed to the main aquarium. In the sump are any of various types of filter media. As a fringe benefit, you can hide the sump in the aquarium stand and attach your water pumps, filters and heaters out of sight. With a sump filter, you only have to worry about hiding the drain and the return pipe, since all of the equipment is installed out of sight in the sump.