The reason for why tides occur at different times is that there are about 12 hours and 25 minutes between two successive high tides or low tides in most locations. There are about half that number, 6 hours and 12.5 minutes, between a high and a low tide.
The length of a lunar day--which is the time it takes for us to see the moon rise, set, then rise again--is about 24 hours and 50 minutes. This variation in lunar day is why tides follow a cycle that is more than 24 hours in length (or more than 12 hours between successive high or low tides).
Tides are caused by the combined gravitational pull of the moon and the sun and are also somewhat influenced by forces resulting from the earth's rotation. Other factors such as ocean currents come into play in some locations. Variation in the magnitude of tides (force) are caused by the relative influence of the sun and moon, depending on how closely the solar tides and lunar tides line up.