The Kill to Death ratio, or KD ratio, is simply a player's number of kills divided by the number of deaths. It's mostly used in FPS and BR games.
The KDA ratio means Kills, Deaths and Assists. The formula for KDA is (Kills+Assists)/(Deaths+1). It's mostly used in MOBA games.
The KDA ratio is part of a series of performance statistics, which may assess a player's performance and/or their approximate level of power, compared to other players in the game.
When referring to ranked modes over an accrued number of games, they may also be used to compare a player's performance with other players' in the same skill bracket.
These performance statistics are not explicitly tracked in-game; they are calculated.
Ratios here are also mathematically undefined for zero deaths. To solve this, by convention either the death count is raised to 1 (i.e. the D in the formulae is replaced with max (D+1), or "zero deaths" is simply considered a "perfect" score.
Here's one example: