Obviously if you are outside the track of a total solar eclipse, you will see only a partial - the further you are from the centre, the less eclipse you will see. But in some cases, the central part of the moon's shadow - the umbra - misses the Earth altogether, and only a partial eclipse can be seen anywhere on Earth. There are more of these than any other type - 35.3% of all solar eclipses. The next one of these will be on 2015 Sep 13, where maximum eclipse occurs over Antarctica; apart from that area, maximum eclipse will be seen from South Africa.
The mathematicians among you will spot that there's 4.8% missing - what are they?
Since the Earth is a globe, the edges of the globe are further from the Sun than the point directly underneath the Sun. Thus as the umbra, or track of a solar eclipse, moves across the surface of the Earth (usually from West to East)*, the point where the shadow hits the Earth will be closer to the Sun near the middle of the track than at its West and East extremities. And since the umbra is a tapering cone, the closer to the Sun we intersect that cone, the greater the diameter of the cone at that point.
Further, since the Moon's distance from the Earth, and the Earth's distance from the Sun, are always changing, at varying rates, and sometimes in opposite senses, then the apparent size of the Moon relative to the Sun can change even during the short duration of an eclipse!
Various combinations of all those factors with an eclipse of short duration can sometimes give what's called a hybrid eclipse - one which is annular along (usually) the beginning and end of the track, but total during part of the central section.
In such cases, the annularity is longest at the start of the eclipse, and gradually decreases to zero as the shadow on the Earth gets closer to the Sun. It will then become total, with duration of totality increasing to the point where the shadow on Earth is closest to the Sun. From this point, as the shadow moves closer to the opposite (Eastern) edge of the globe, the duration of totality decreases, reaches zero, and then the eclipse becomes annular again until the shadow passes off the Earth altogether.
Very rarely, such an eclipse can start as annular and become total but without reverting to annularity again (or vice versa). This happened with the eclipse of 2013 Nov 03 which started as annular in the west Atlantic off the coast of Florida, quickly became total with maximum eclipse off the coast of Africa, and remained total, although with decreasing duration, until the eclipse ended in Ethiopia.
* The rare circumstances when it moves more S to N, or N to S, or even slightly 'backwards' are too complex to describe here!)
Terry Moseley, 2015