German postdoc salaries (TV-L E14) What does "TV-L (E14, 100% position)" mean in terms of gross and net pay? What lifestyle does this buy you in Berlin?

This is in the context of a postdoc at a research institute.
You are right that TV-L is a civil servant payscale. Postdocs commonly are placed in the E-13 or E-14 scale, where the latter is higher (but usually comes with more responsibilities). The gross pay starts at just under 3579.34 EUR per month for Berlin. Very recently the pay scales have been renegotiated, so I believe it might have gone up a bit. This amount is the first step in the scale, depending on your experience you might start at a higher step.

The net amount depends on your specific circumstances, for example if you are married and if you are a member of a church. For single persons that are not registered with a church the net amount is around 2100 EUR a month. This includes health insurance. You should be able to live decently in Berlin for this money.

The details can be found on the Öffentlicher Dienst website  (in German, but you would want the table at the bottom).