Apoyando is a method of plucking used in both Classical guitar and Flamenco guitar known in English as 'rest stroke' (a direct translation of 'apoyando' would be "resting"). Rest stroke gets its name because after plucking the string, the finger rests on the adjacent string after it follows through, giving a slightly rounder, often punchier sound (contrasted with tirando). The apoyando stroke is not intuitive so is rarely used by beginners. Most players will use the tirando or 'free-stroke' and will have difficulty in managing the apoyando.
Towards the very end of the 20th century up to today, many professional classical guitarists developed a strong preference for tirando and have moved away from thinking of apoyando as the main basic principle of guitar technique.