This is done so that you can have large bouquets yet a thin handle. The disadvantages of doing this is that as the flowers have no water supply, the work must be done very last minute. The second technique that goes by the same name refers to wrapping a wire around the stem of flowers so that even if the flowers wilts, the wire will hold it up. It is not necessary however if you don't want to worry about anything the day of the wedding, it might be worth doing the outer flowers in a bouquet. Corsages and boutonnieres are not difficult to make.
Corsages are essentially multiple boutonnieres attached to each other.
If you were making rose boutonnieres or corsages for example, you take florists wire and insert it through the green base of the rose. Bend the wire to form a hairpin. Then wrap florists tape in a spiral down from the top. When the wire 'stem' is as long as you want it to be, cut it. If you want to add greenery or babies breath, then attach the sprig and tape it onto the wire stem.