With a rifle scope when you see numbers describing the attributes of the scope like 2-7×32 they tell you quite a bit about it’s capability and what the scope can be best used for.
The 2-7 means first that the scope is a variable power scope where the magnification can be adjusted from 2 power to 7 power. At 2 power the the target appears 2 times larger from your point of view with your naked eye .
At 7 power the target appears 7 times larger. These numbers also tell us that this scope can be adjusted to any magnification between 2x and 7x depending on your needs for the shot. If the numbers are 7×32, you are looking at a fixed power scope.
When looking through the scope the target will appear 7 times larger than with your naked eye. Magnification on a fixed power scope again is fixed and has no adjustment to increase it. The 32 means that the objective lense is 32 mm in diameter.
The objective lens is usually at the larger end of the scope, opposite the ocular lens which is the lens you look through.The purpose of the objective lens is to transmit light to the ocular. The larger the objective, the more light it can transfer.
When searching for a scope that could or will be used in low light conditions, like a hunting scope, you want the largest objective lens you can find. If all you will do with it is shoot during well lit situations a smaller objective will work.
Other factors come in to play when choosing a scope for a particular purpose. For more information on that check out this article