First number is the magnification of the eyepiece. Second number is the diameter of the objective lens in mm. Hence 7 x 50 is a pair with 50mm objective lenses and eyepieces having a magnification of 7 times.
Some top end binoculars allow eyepieces to be interchanged to give different magnifications - often using standard 1.25" oculars.
You will often see identical looking binoculars for sale with different magnifications - often at the same price. Eg 25 x 100 and 30 x 100. Just different non-removable eyepieces fitted.
Some binoculars have a zoom mechanism in the eyepieces allowing a range of magnifications - say 7-30 x 50.
They are often also marked with the field of view. Sometimes in degrees but often in the form of the width of the image in feet at a distance of 1000 yards (or width in metres at 100 metres).
Read up here:-
http://www.aoe.com.au/binocular_guide.html