The word "sprite" is interesting. It means elf, fairy, or ghost, although it can also refer to flashes of different color lights in clouds caused by lightning. The word originated in the middle ages from the word "spirit". When I hear the word, I think of the Disney character Tinkerbell.
In computers and video games, a sprite is an image that can move on top of a background. Usually, these are 2D objects moving on top of a 2D background, although a game like the original Doom had 2D objects moving on top of a 3D background. The mouse pointer on a computer screen is technically a sprite.
Back in the days when computers and video games were 8-bit and 16-bit, it was helpful to have hardware support for sprites, which allowed graphical objects to move around independently of the background. The reason this was helpful was that it was more taxing for the old slow computers without hardware sprites to manipulate the graphics on the screen. When I was writing games for the Timex Sinclair 2068 and Atari ST computers, I had to write software to make all the graphics move because there was no hardware support for sprites, which makes the task more technically challenging.
The early arcade video games used hardware sprites and so did all early home video game consoles. The sprites on the Atari 2600 are extremely primitive and very difficult to program, but the programmers knew how to make them work.
Many people have touted the Commodore 64 as the best 8-bit computer because it had hardware support for eight 8x8 sprites, although this is not very many compared to the Nintendo Entertainment System that came out later. I think that the Atari 8-bit computer had better graphical capabilities overall.
Once we had 32-bit processors, there was no longer a need for hardware sprites. These systems were powerful enough that it was not a huge challenge to manipulate graphics on a screen. Also, with 32-bit systems, there was a greater emphasis on 3D graphics instead of 2D graphics.