It's normal to experience muscle pain after exercising if it's been a while since you were active or performed a certain movement. This type of pain - called delayed onset muscle soreness or DOMS - generally develops several hours later and exacerbates over the next few days.
The exercise that induces DOMS consists of eccentric (lengthening) muscle contractions in which contracting muscles are lengthened. Walking down a set of stairs or slope, where front thigh muscles are lengthened when supporting the body weight, is one example of eccentric exercise.
Another is using weights, such as a dumbbells. When lowering a heavy object slowly from an elbow flexed to an extended position, the muscles to flex the elbow joint perform eccentric exercise, since the external load (dumbbell) is greater than the force generated by the muscle.
Exercise consisting of mainly concentric (shortening) contractions, where muscles contract and are shortened, such as walking up stairs and lifting a dumbbell, does not induce DOMS at all.
DOMS is technically considered an indicator of "muscle damage", as muscle function decreases and, in some cases, muscle-specific proteins increase in the blood, indicating plasma membrane damage. But it appears that very few muscle fibres are actually injured or destroyed (less than 1% of total muscle fibres).