People who like to amass gamerscore points on Microsoft's XBOX 360 console (also referred to as "Achievement Hunters") tend to divide Achievements into a couple of different categories. There's the "easy Achievements " category, which contains Achievements that are almost too easy to get and popularize certain games among the Hunters (for example, Avatar: The Last Airbender: The Burning Earth). You've also got the "unmissable Achievements", the ones that you get by simply playing through the levels/main storyline missions a game forces you to go through, such as all the Achievements in King Kong.
Certain Achievements can be gained at a single point in the game, and if you fail to fulfil their requirements at that point, then you must replay the entire game to that point to get another shot at attaining them. For example, Assassin's Creed II has an Achievement called " Fly Swatter". It requires the players to kick a guard while they are flying around with the flying machine, but the players only has access to this machine during a single mission in the game. After the mission is over, they'll never be able to fly it again. So, if those opportunities to kick a guard are missed, Assassin's Creed II's lack of a level select feature forces a player to replay the game. This specific complaint was so numerous that one of the features added in the first DLC released for the game was the ability to use the flying machine whenever the player desires.
This is an important feature of a missable Achievement. If a game has an Achievement that can only be gained at a certain point, but does have a level select feature which allows the player to get to that point without spending too much time playing to get there, then that game does not count.