One of the traditional reasons is to obtain a very high CO2 concentration in the beer. I'll let Charles Graham explain.
"There remains, however, a still more important factor in giving fulness to beers of medium original gravity, and that is the carbonic acid. Beer cooled to a few degrees above the melting point of ice must necessarily contain more carbonic acid than at 60° F., which may be taken as the average temperature of English beer as consumed. We all know that draught or bottled ales, if allowed to stand some hours, become insipid and flat, and taste as if several pounds per barrel less in the original gravity. The important influence of carbonic acid in making beers taste fuller and rounder has long been carefully attended to by the German brewer, whose great aim has been to secure as large an amount as possible. Hence an important part of the duty of a German brewer is to have his beers in perfect condition in the cellar, so that with a fortnight's closing of the bung- hole, a sufficient amount of carbonic acid shall be formed and retained. For the same object one often finds in restaurants and beer kellers, air or carbonic acid forcing pumps to increase the amount of gas when the beer becomes too flat. The greater amount of carbonic acid in German beer is partly due to the greater amount of saccharine and albuminoid matters, but chiefly to the low temperature. The influence of temperature in the lager cellar upon the amount of carbonic acid has been the subject of some experiments by Professor Langer and Dr. Schultze. The beer they experimented on was made from a wort showing 10 degrees Balling, and had been attenuated 60 per cent. The carbonic acid found in 100 volumes of beer was at—
0.4º C 0.332 by weight 100 volumes by volume
1.6 º C 0.320 by weight 96.4 volumes by volume
2.8 º C 0.311 by weight 93.7 volumes by volume
4.0 º C 0.297 by weight 89.5 volumes by volume
4.7 º C 0.285 by weight 85.8 volumes by volume
Thus an elevation of 4'3° C. in the cellar temperature reduced the carbonic acid by one-seventh of the original volume, or nearly 15 per cent Hence the reason for keeping the temperature of the lager cellar as low as possible ; so that more carbonic acid may be kept in solution."
“Journal of the Society of Chemical Industry” 1882, page 31.
Did you spot the early reference to top-pressure dispense? I wonder why no-one uses the expression "carbonic acid forcing pumps" today? It sounds so much more quaint than "keg pump". Those silly Germans. Didn't they realise the inherent superiority of cask beer?
Thanks to Gary Gillman for pointing out this article to me. You can never know too much about Lager.