Spring tides are a periodic phenomenon that occurs when the sun, moon and Earth are aligned. If you drew a radial line outward from the sun, it would pass through the center of both the Earth and the moon during the spring tide. This can be accomplished in two ways; the moon can be between the Earth and sun, or the Earth can be between the moon and sun. The former circumstance would naturally produce stronger tides than the latter, as the sun and moon are both pulling in the same direction, whereas the latter occurrence would still produce higher than normal tides, but not so high as the sun-moon-earth alignment.
The perigee is the point in an object's orbit where it is at its closest point to the body that it orbits. More properly speaking, the "gee" in perigee implies that the central body is the Earth, and so anything orbiting the Earth with any degree of eccentricity will have a perigee (and its counterpart, an apogee). Normally the suffix would change depending on the central body - for example, something orbiting the sun should have a perihelion rather than a perigee for that relationship, but sometimes the term perigee is used a bit loosely.
The perigee would result in the gravitational force being stronger than at any other time in the object's orbit. You can demonstrate this through the use of Newton's Gravitational formula; F = G(mM/r^2), where the force increases exponentially as the distance (r) decreases.
If the perigee coincided with the spring tide, then the tide would be even higher than a normal spring tide, but the extra height would be on whichever side the moon is, because its gravitational force is what has changed the most.