Low federal funds rates allow companies to acquire huge amounts of debt very cheaply.
Huge amounts of cheap debt allow companies to buy lots of stock, driving up prices.
Stock prices inflated in such a way are not supported by fundamentals and so the downside risk greatly increases.
Once the downside eventually materializes, markets drop violently. At first, the FED ignores this, but eventually it bails. The funds rate is once again lowered, so the game can continue.
In any event, the game must continue, because companies need new debt to service old debt. If the new debt was more expensive, the companies would eventually risk defaulting.
To understand the risk of corporate defaults, one must look at the importance of corporate bonds in pension funds. Ironically, the low federal funds rate is part of what drives pension funds to purchase more risky corporate debt, in order to meet their yield requirements.
All of this causes massive asset price inflation. Stock prices are detached from actual revenue, real estate prices are detached from rent income. The rich are getting richer - at least on paper - because they own most of the assets.
The CPI doesn't immediately reflect this kind of inflation, so the FED gets to claim "there is no inflation" and everything is "just fine". Well, it's not fine and they know it, they just can't really do anything about it.