Intensity depends on the strength, or amplitude, of the vibrations producing the sound. If a piano string is struck forcefully the string swings back and forth in a wider arc. The stronger vibration then produces a louder tone since stronger vibrations compress the molecules of the air more forcefully and gives them greater energy, which is interpreted by our ears as a louder sound.
The loudness of sound is largely subjective, the ticking of an alarm which is perceived as quiet during the day can seem annoyingly loud during the night as can a distant burglar alarm even though in reality the "noise" is small. Loudness is measured in decibels (dB) which is the ratio of the intensity of the sound to that of a standard sound of 0.000 000 000 001 watts/sq.metre at 1000 Hz which is just about the faintest sound that a typical young person can hear. A sound ten times as intense as this standard sound is rated at 10 dB or 1 B (Bel).
Loudness talks about the frequency and intensity is the amount of sound passing thru a unit area per second.