While the term was popularized by Super Smash Bros. Melee, wavedashing is a term used in competitive circles to refer to two distinct applications detailed below. Both of which produce momentum and slide while being able to perform other actions.
Starting from the air
One implementation is especially common in platform fighting games like Melee (the only official Super Smash Bros. instalment have it), where it allows the player to jump then use the inertia from a directional air dodge to slide on the ground.
The distance is determined by the angle chosen plus the character's traction with the ground. Hence, Luigi, known for being slippery in platforming games, can gain more distance than others. However, there is also a "Perfect Wavedash" where the character immediately slides by cancelling the jump squat animation rather than air dodging from mid-air.
This technique is useful due to the many possible distances as well as being able to access the whole grounded arsenal of options as the state is considered to be standing including a jump, this differs from dashing which can be jumped out of but limits grounded attacks to the Dash Attack, Dash Grab and select B moves. One can also "Waveland" by deliberately using the technique while landing to mix up landing movement options (especially with platforms).
While, this mechanic wasn't carried over into the sequel, Super Smash Bros. Brawl, the mechanic lives on through both mods of Brawl (through "Project M") and Smash for Wii U/3DS (through "4XM") and numerous indie titles inspired by Melee like Rivals of Aether. Another example is WaveLand, a speedrunning focused platformer, where the player can use wavelanding on walls and ceilings as well as wall jumps to pick up speed.
Rocket League supports this version of the mechanic as incomplete barrel rolls or flips can have their inertia carried into a power slide. This is especially handy as players can use this gain a lot of speed without using Boost or regular acceleration allowing quick recovery and tricky movement.
Exclusively from the ground
Another common implementation can be seen in the Marvel vs. Capcom series and Tekken series. In Marvel, characters can use this to cancel their dash into a crouch while sliding to use of grounded options earlier and control distance. A similar implementation is used in Knight Club despite it being a platform fighter.
Wavedashing in the Tekken series isn't a universal option but offers the benefit of being able to cancel crouch dashes into each other which can serve to buffer inputs and to extend the range of attacks.