Ultimately, all the drains in your house connect to a single line which then emptoes to either a sewer system or a septic tank. Those lines are susceptible to being invaded by tree roots over time, which is the whole basis of the industry from which the Roto-Rooter company derives its name.

While plastic drain is less susceptible to root invasion than the older tile pipes (the joints are tighter), root growth is eventually inevitable. The presence of a big tree anywhere near your drain increases the likelihood, obviously. The only way to know with certainty that root growth is the problem is to have your pipes "scoped", which is a process in which a plumber puts a long, flexible, lighted telescope down into the drain and actually looks to see what's there. Of course, there is a fee involved.

If substantial root growth is present, the pipes should be "roto-rooted" (there's probably a more technical name for this!) In essence, a big rotary cutter is run down the pipes and the roots are choped up and flushed out. There is a risk of damage to the pipes from this process, and cutting roots can be a gold mine for an unscrupulous plumber, who then ends up with a drain replacement job rather than a root cutting job. Yard gets dug up, smelly, dirty work, etc, etc. BE CAREFUL out there!

Another possibility is that baby wipes - those soft, pre-moistened towellettes - have plugged up the drain. Most people don't realize that the wipes, generally, are not biodegradable, so even flushiong away just a few can eventually clog up the drain as they get caught on even minor root growth, or even rough sections of the home's internal plumbing. Some wipes state on the can that they are flushable (most don't, and aren't), but read the fine print - it warns against flushing more than one or two.

If you have been flushing baby wipes, you may be able to use a "plumbing snake" to remove them if they have clogged up relatively close to the toilet.

As I mentioned intially, it may just be that the pool backflush overloaded an otherwise healthy drain system, especially if the pool was added on later rather than built as part of the initial home spec.

Your options:
1) Quit flushing baby wipes.
2) ignore the problem as long as it only occurs with pool backflushing. You may be OK for 10 years, or 2 weeks.
3) Try snaking your internal plumbing. Since the basement bathroom is likely the lowest drain in the house, try snaking through the basement toilet. You may well do slight damage to the porcelain in the toilet bowl; if you're concerned about that and ambitious, you can remove the toilet and snake from the hole (see www.toiletology.com - really!) Snaking is moderately difficult and dirty.
4) Call a company who can scope your drains. You probably do 3) first and, again, make sure that you get multiple good references before you call a company. Demand that they provide an extensive reference list, as well. If you live in a larger city, try consulting www.angieslist.com.

Right now, you have a minor problem. Over time, drain root invasion is nearly inevitable, but you may be years (or weeks) away from an absolutely necessary repair. Use your judgement. Good Luck.

Al