Sprites and Textures are both images.
A Sprite is an image that can be used as a 2d object, which have coordinates (x, y) and which you can move, destroy or create during the game.
A Texture is also an image, but that will be used to change the appearence of an object. E.g. you can set a texture for the faces of a cube, a layer (like the background) or even a sprite. But as texture are not objects, you can't move them during the game.