An operational feature of firearms this term can have one of two meanings:
1) (Normally in pistols) Pulling the trigger of the weapon only serves to fire the weapon and does not cock it as well (that would be double action). Whether the weapon re-cocks and reloads itself afterwards depends on the rest of the design (for example some early revolvers needed to be manually re-cocked after every shot, whilst a modern self-loader will have at least a semi-automatic action). The weapon must be manually cocked before firing in any case, and this action often serves to chamber the first round. This is normal in early pistols and many designs of self loader.
2) (Normally in long arms) The weapon must be manually re-cocked and re-loaded after each shot, and whilst it may be magazine fed, it does not self-load. Examples of this form of single action include:
Technically a muzzle loading weapon is single action by necessity, but the term is usually redundant in this context.