Let's start with the ideal situation. Suppose you have enough income and low enough expenses to do the following:
-max out your 401k ($23k)
-max out your Roth ($7k)
-park the rest of your savings in a taxable brokerage account
-invest all 3 accounts in a stock-heavy portfolio, such as 100% VTI or 80/10/10 VTI/BND/GLD.
For a W2 wage earner under age 50, this is about as good as it gets. You're maximizing both tax shelters. Money that piles up in the taxable account can be used for major future expenses, such as a new HVAC, car replacement, or roof replacement. Until those expenses become necessary, this account earns an aggressive portfolio's rate of return.
In the event of an income disruption like a job loss and 6-12 months unemployment, the taxable account can either serve as an emergency fund OR send money to the Roth so you don't miss the opportunity to contribute that year. If your income disruption corresponds to a bear market, you might enjoy tax loss harvesting as part of your process of moving cash to the Roth. Then buy a similar fund in the Roth and never pay taxes on the future gains from investments bought for cheap during a bear market.
For those of us not saving over $30k per year, I think this ideal situation is still instructive. You want to max out your 401k first and foremost, to minimize taxes. But those with early retirement intentions may also want to build up a decent Roth balance to obtain flexibility over their taxable income in retirement and to keep their Roth ladder conversions in the low brackets.
I see a taxable account as helping to compromise between these goals, it's an emergency fund, a planned expense fund, a staging ground for Roth deposits in the bad times when earnings are insufficient to optimize IRAs, and an overflow container in the good times when earnings are far exceeding expenses. There's no one way to use a taxable account because it is a multipurpose tool with different applications depending on what's going on.