The tides are created by gravitational pull of the moon and, to a lesser extent, the sun, on the ocean waters. At full moon and new moon, the moon and the sun are aligned (their gravitational pull is in the same direction), so the tides are stronger. At first and third quarter moons, the moon and sun are pulling in opposite directions, so tides are weaker. Seasonal variations in the tides happen because the Earth moves closer to or farther from the sun during its elliptical annual orbit around the sun, and the sun's gravitational pull is stronger when the Earth is closer to it. Similarly, the moon's distance from the Earth varies with its eccentric (irregular) orbit, introducing more variation to the tidal patterns. For more details about what controls the tides, look at the complete tutorial by the National Ocean Service.
As the moon orbits the Earth, its position relative to the Earth and sun varies: sometimes it is (roughly) in a straight line (Sun - Earth - Moon or Sun - Moon - Earth), and sometimes it is next to the Earth, forming a triangle between the sun, moon, and Earth. One orbit of the moon around the Earth is a complete lunar cycle. So why does it appear to us on Earth that the face of the moon cycles between darkness and illumination as it moves through its orbit? The reason is that from Earth, we can only see the side of the moon that faces the Earth, but the side that faces the sun is always the illuminated half. The more we share the sun's view of the moon, the more illuminated the moon appears to us. When the moon is between the Earth and the sun (in a Sun - Moon - Earth straight line), we only see the dark side of the moon, a new moon. When the moon is off to one side of the Earth in a triangular arrangment, it appears to us that the moon is partially illuminated. Finally, when the moon is on the opposite side of the Earth from the sun (in a Sun - Earth - Moon straight line), we share the Sun's view and can see the whole illuminated side of the moon (full moon). In the Sun * Moon * Tide calendars, notice that the moon is up at night when it is full, and the moon is up in the daytime when it is a new moon. This makes sense when you understand the geometric arrangements involved. For a complete explanation of moon phases with lots of diagrams, see Nick Strobel's Astronomy Notes.
The sun intensity (also called the insolation) is the sine of the sun's altitude angle. It is the power per unit surface area of the sun's radiation. Sun intensity is the best way to measure many things, including: