The graphics you will use in your own games are made up of images called sprites or 3D models which are textured with images depending on the type of game you will be making. I will tell you more about them and show you how to get professional sprites and 3D model textures you can use when making a game.
The art used in 2D games is often referred to as a sprite. A game sprite is a picture or image that is used in the game to create the visual appearance. For example if you have a platform made up of grass for the player to walk on then the grass image will be a sprite. Game sprites are used to make up the look of the levels and characters of most 2D games.
The graphics in 3D games are different because the characters and most of the environment is made using 3D models which have been painted using textures. A texture is an image that is wrapped around the 3D model and many 3D models can have multiple textures but unlike sprites used in 2D games a texture will often be much larger and contain more detail.
You can download textures and models online. There are some websites offering game graphics for free while other websites are selling the game graphics. OpenGameArt.org is a good place to download free textures and sprites for your games and has a large range of art contributed by the community pf users on that website. For developers looking for a rage of commertial sprites and game assets I recommend GraphicRiver because there is some good quality game art there ready to us in your games.
The game engine you are using should also have some sort of store that will sell or give away game objects, sprites, textures and other things to use in your game so always look there first, A great example is the Unity Asset Store which is the go to place for people using the Unity3D because it is built into the game engine software and has some of the best game graphics available to purchase and use right away.
When you download game graphics it is important to make sure you are allowed to use it and you should know what the terms of using that art work are. Most websites offering game graphics to download will clearly show you the license terms and if you can not find them I recommend you don't use the art in anything that will be released to the public and avoid legal complications because of copyright violations.