What is the significance of amphidromic points related to tides?
This will be a bare-bones answer, because I don't have time to do more. If somebody wants to do a more complete answer, with a figure or two, feel free; otherwise I'll try to come back and expand this in a day or two

Good question! If one is familiar with the simple explanations of tides (bulges of water following the moon around the earth), this doesn't make sense. 
However, that way of thinking only gives us equilibrium tides, which are what we would have if Earth was an ocean planet. In reality, we have continents, and they get in the way.

Most tidal movement actually consists of water "sloshing" around ocean basins - e.g. across the Atlantic between North America and Europe. But because the planet is spinning, Coriolis force applies and tends to impart rotation to straight-line movements. This results in the tide tending to form two-dimensional waves that go around ocean basins in a roughly circular pattern. You can get a similar wave going in a hot-tub, with a bit of effort! At the outside of the basin, where the wave meets the land, the amplitude tends to be the greatest - but in the middle, it's close to zero.