How is the process of natural selection involved in evolution?

Natural selection means that the organisms better adapted to their environment, that is, they have developed the right characteristics/skills/response to the external ambient, have higher chance to survive, making the next generations genetically inherit such acquired surviving characteristics.
These generations will thus have a higher chance of survival, making these species being "naturally selected" as survivors, while those who haven't or are slower in this process, have a higher risk of elimination.