A focal reducer does just what its name says: it reduces the effective focal length of your telescope. It also reduces the f-number of the scope and decreases the magnification of eyepieces used with your scope. It increases your field of view, too.
To calculate the increased field of view, start with the eyepiece’s apparent field of view supplied by the manufacturer. Divide by the magnification. Now take this base true field of view in degrees and divide it by the reducer’s factor. The standard Celestron f/6.3 focal reducer has a 0.63 reduction (compression) factor.
As an example, a Celestron Ultima 32 mm eyepiece has an apparent field of view of 70 degrees. It gives a magnification of 87.5x with an 11 inch, 2800 mm Schmidt-Cassegrain telescope (SCT). So the true field of view is 70/87.5 or 0.8 degrees. Screwing on the f/6.3 focal reducer increases this field of view to 0.8/0.63 or 1.3 degrees.
Note: Even though the true field of view is increased, you may very well have vignetting when using focal reducers with long focal length and/or wide-field eyepieces. This is especially true with the smaller SCTs (5, 6 and 8 inch).