The context of this line is Lady Bracknell's interrogation of Jack, as she tries to discover whether he would be a good match for her daughter. She asks him a number of questions, and most of his answers are satisfactory, up until he mentions being found in "A HANDBAG?!"
At this point, she asks him whether his income is "in land" or "in investments". He replies that it's mostly in investments, and this is one of his satisfactory answers: she responds with the quote from your question. She is complaining about taxes on land:
the duties expected of one during one’s lifetime
This refers to property tax, paid by landowners during their lifetimes.
the duties exacted from one after one’s death
This refers to inheritance tax, paid by a landowner's estate after their death.
land has ceased to be either a profit or a pleasure. It gives one position and prevents one from keeping it up.
In the society in which this play is set, ownership of land is required for social status (it "gives one position"). But Lady Bracknell is complaining that the taxation on landowners is so heavy that it "prevents one from keeping up" that social status, by bleeding one dry of money. Hence her conclusion that it is better to have one's income from investments than from land.
It's also useful to set this in historical context. During the second half of the 19th century (in which The Importance of Being Earnest was written), there was a lot of debate between leading British politicians, notably Disraeli and Gladstone, about taxation. It's probably very realistic that a woman like Lady Bracknell (a Conservative, who would have supported Disraeli) would be complaining about taxation. You can read a good summary here on Wikipedia. For example:
Disraeli and Gladstone agreed about little, although both promised to repeal income tax at the 1874 General Election. Disraeli won – the tax stayed (and probably would have done under Gladstone too). Gladstone spoke for nearly five hours introducing his 1853 Budget. He outlined plans for phasing out income tax over seven years (which the Crimean War was to upset), of extending the tax to Ireland, and introduced tax deductions for expenses 'wholly, exclusively and necessarily' incurred in the performance of an office – including keeping and maintaining a horse for work purposes. The 1853 Budget speech included a review of the history of the tax and its place in society, it is regarded as one of the most memorable ever made.
With the Whigs defeated in 1858, Disraeli returned as Chancellor and in his Budget speech described income tax as 'unjust, unequal and inquisitorial' and 'to continue for a limited time on the distinct understanding that it should ultimately be repealed'.