Transistions is a brand name from Essilor that is one of the most advanced and also most popular types of photochromatic lenses for glasses and spectacles.
The name itself sounds quite complicated, and although the process was discovered in the late nineteenth century, the use in spectacles is a fairly modern application. There is no rigorous definition beyond a “reversible change of colour upon exposure to light” but there are wide differences in the effect depending on the compounds and materials used in glasses and lenses.
There are always trade offs to be made when choosing glasses, and particularly when you are comparing the prices for glasses with such features whether online or on the high street. Consider what attributes of the glasses are most important for you and the way that you intend to use them - for example some spectacles with transitions (or other brand photochromic) lenses are much better in cold temperatures than warm temperatures.
The speed at which the glasses themselves go dark varies greatly between the different brands - an easy way to compare the “quality” is to measure how quickly the glasses go from being dark to light (as opposed to when the glasses go from light to dark) - as this is much harder to do chemically.
One final thing to consider if you are thinking of transitions type glasses is that they do not perform well for driving - as they require exposure to direct sunlight (specifically UVA &B) in order to turn dark, and of course the windscreen in your car does a great job of filtering out this part of the electromagnetic spectrum to protect your eyes. So if you are looking for glasses for driving, consider instead buying two pairs of cheap spectacles online - one pair as clear or a slight tint, the other as sunglasses with a dark tint in the lens, and switch them depending on the driving conditions.