1 : a balancing of factors all of which are not attainable at the same time
2 : a giving up of one thing in return for another
The article says the biasing form "increases the input impedance", but also "reduces stability" (due to gain reduction from feedback). So it's a trade-off between these two factors. You can't have both, so you have to decide if it's OK -- if it's warranted -- for your application to be less stable.
There are many such trade-offs everywhere. In civil engineering, for example, you can make a bridge more sturdy, but doing so makes it less flexible. Or more expensive. A computer application can be made faster, but only as a trade-off for complexity.
In everyday life, you can trade off having a larger house, farther away from the city, for having a longer commute to work. Or buying a smaller house, as a trade-off for a lower mortgage payment. And so on.