The significance of this hadeeth is that science has recently verified this process of embryo/foetus development. That is, six weeks (roughly 40 days) after fertilisation, the embryo is developed (from zygote - sperm & ovary - to embryo); then another 6 weeks (roughly another 40 days) it develops into a foetus (a clot); after which for about the same period (again roughly another 40 days) it develops into the recognisable human form (a blob of flesh). 

Science has also verified that the foetus can think. Before 120 days the foetus does not think: "The brain of the foetus appears to be electrically silent during the first six weeks of life. After this time, slowly activities of low intensity occurs. So although the brain is at least 'moving', it is not 'thinking' in any real sense." (The Thinking Foetus) But after 120 days, when the spirit (ruh) enters the foetus, brain activities place: "The foetus becomes conscious sometime during the second trimester...There is ultrasound evidence that about 23 weeks (161 days) the foetus dreams. Dreaming is certainly an indication of the presence of the mental capabilities required for thought..." (The Thinking Foetus) 

There are numerous other things which the foetus can do in this period. Such as expressing emotions (happiness, fear, disgust etc.) through it's facial expressions. It can show anxiety through the sucking of the thumb, assert itself and protest through kicking, and it develops memory.  
One other important development during this stage is the ability to distinguish and recognise sounds. Experiments have been carried out that proved this: - A newborn will prefer a story that has been read twice a day to it, when it was a foetus, to a new one.  -  A newborn will recognise and copy its mother's words.  -  When a theme music to a program was played, a newborn whose mother watched the show during pregnancy, will calm down.

What is significant about this is that babies can be taught the Quran (or some surahs (chapters) from the Quran) while they were in their mother's womb. 

Imagine if you were to read the Quran everyday to your foetus, by the time it is born, inshaa Allah, it will prefer the Quran over other books and sounds. It will recognise the Quran and try to copy it, and it will use the recitation of the Quran to find solace. Is that not what we all want for ourselves, let alone for your child? Imagine your reward when you have bestowed, with Allah's Grace, this tremendous gift on your child. Your reward will be two-fold: one for you for reciting the Quran, the other for you and your child for having taught him the Quran. 

Even if you cannot read the whole Quran, whatever you can read, inshaa Allah, will benefit the both of you. A few surahs twice a day will engender a love of the Quran in your child.