Sprites are graphics used for Things.
Some things, such as certain powerups, look the same from all angles but cycle through several different appearances as time passes. Each of these has several sprite graphics, displayed in a rotating sequence at a controlled rate.
The most complicated things, monsters and players, look different from different angles and can have their appearances altered by various gameplay developments. Each of these has a somewhat larger set of sprite graphics, for which the display sequence is determined by the Doom rendering engine. In Doom, exploding barrels are also handled this way.
Each Doom engine thing has a four-character sprite prefix defined for it, and all of its graphics are named beginning with this. The fifth character of a sprite graphic name gives the animation frame ordinal, starting at A and proceeding through the alphabet. (The sequence continues past Z, if necessary, using ASCII encoding.)
The sixth character of a sprite graphic name gives the rotation or rot. If it is 0, the graphic is used for all viewing angles. Otherwise, eight graphics, with sixth character ranging from 1 to 8, must be defined. The graphic 1 is used to draw a thing looking head-on; 2 through 8 are used as the thing is rotated in 45-degree steps clockwise (as viewed from above). Note that in some source ports, such as EDGE, PrBoom+, and ZDoom, this system is expanded to 16 angles, in 22.5-degree increments, using 1-9 and A-G for the additional sixth-character angle names.
It is possible to use a single graphic for two rotations. For example, the name TROOA2A8 defines a graphic with prefix TROO for animation frame A rot 2. The same graphic, drawn in mirror image, is used for animation frame A rot 8.
Replacing sprites using a PWAD file presents certain problems in the original Doom engine, as all sprites must be in a single continuum between S_START and S_END; and any lump that does not respect the sprite naming convention found between these markers will make Doom abort on startup with an error message. This means that the PWAD must contain all IWAD sprites, even if they are not modified, or they will be invisible. Starting with Boom, source ports started allowing several sprite ranges each between their own S_START (or SS_START) and S_END (or SS_END) markers.
Boom also introduced an invisible sprite, TNT1A0.
Additional detail is given in the Unofficial Doom Specs.