I was reading an old AMA on Reddit with Peter Wolfe, a brewing scientist at Anheuser-Busch Technical Center, and I came across his response to a question about beechwood aging:
"In the olden days (mid to late 1800's), people didn't fully understand how yeast worked, they just knew they needed it. They also weren't really good at making consistent batches of malt. The combination of these two things meant that lager beers would often stall out before they finished fermenting because the yeast would prematurely flocculate.
To help offset this, the brewers of the day would line the bottom of the tanks with beechwood (which look like this). The wood acts as a matrix for the yeast to adhere to and prevents it from forming a solid sediment layer on the bottom of the tank. This encouraged the yeast to "finish" the beer and bring the sugar levels all the way down and the alcohol levels up. The wood itself provides no flavor (in fact it is vigorously boiled to remove any trace of flavor before it's used), it's merely acting as a cellulose matrix to emulate a bioreactor. I should mention that Anheuser-Busch wasn't the only brewery doing this back in the day; almost all the breweries in St. Louis and many others around the country were.
At some point (I couldn't pinpoint when, likely in the '60s), brewing science had advanced enough that they didn't technically require beechwood anymore to attain the same degree of fermentation. However, it provided a backup against the possibility of premature flocculation if something went wrong, and it was a venerated tradition, so they kept doing it. It's still done today. It does speed up secondary fermentation slightly, but we could make beer without it. We continue doing it for the same reasons they did in the 60's - it still does help and it's a venerated tradition.
TL;DR - prevents premature flocculation...so the yeast can last longer."