It is certainly true that he died on this day: 23 April, 1616, aged 52. This is stated in a memorial on the wall of Holy Trinity Church in his birthplace of Stratford-Upon-Avon.
As for his birth, all we know for sure is that he was baptised on 26 April, 1564 – this is in the parish records. Christenings were usually held very soon after the birth because so many babies died, so Shakespeare is unlikely to have been born more than a few days before this date. Therefore the date of 23 April is perfectly possible – even quite probable – but not certain.
The tradition probably arose because St George is the patron saint of England, and Shakespeare is generally regarded as the quintessential English writer, exemplifying all that is best in the national culture. The idea that his life both began and ended on the saint's day is so attractive that everybody wants to believe it, although we will never be sure.
As for his birth, all we know for sure is that he was baptised on 26 April, 1564 – this is in the parish records. Christenings were usually held very soon after the birth because so many babies died, so Shakespeare is unlikely to have been born more than a few days before this date. Therefore the date of 23 April is perfectly possible – even quite probable – but not certain.
The tradition probably arose because St George is the patron saint of England, and Shakespeare is generally regarded as the quintessential English writer, exemplifying all that is best in the national culture. The idea that his life both began and ended on the saint's day is so attractive that everybody wants to believe it, although we will never be sure.