Spring tides:
New Moon and Full Moon
The sun, Earth, and Moon are all roughly in the same line.
The gravitational effects of the sun and moon work in the same direction,
bringing higher high tides and lower low tides.
Neap tides:
First Quarter and Third Quarter Moon
(a week after New Moon and a week after Full Moon)
The sun, Earth, and Moon form a right angle.
The gravitational effects of the sun and moon work across each other, bringing
high tides that aren't quite as high, and low tides that aren't quite as low.
There are a pair of gravitational forces trying to pull the Earth and Sun together,
and another pair of gravitational forces trying to pull the Earth and Moon together.
So the Earth's oceans are pulled toward both the Sun and the Moon.