Origin
Taekwondo is a quite modern Asian martial art and its original is found just after world war II. In fact it is a mix of several traditional martial arts: traditional Korean Taekyon and Japanese karate.
Taekwondo is known for its elusive and impressive high kicks.
As it comes to sparring Taekwondo has been professionalized over the last 30 years, although this sport is suited for everybody: as athlete, sparring competitor or as Olympic professional. 
The roots of Taekwondo are Korean.
Korea has been occupied by Japan and was influenced by Chinese culture.
It is a reflection of the history: the Korean leg techniques are in, mixed with Chinese and Japanese (karate) arm techniques.

How TKD changed from a martial art into a modern (Olympic) sport.

Taekwondo is defined as martial art or budo sport.
'Bu' means 'military affairs', whereas 'do' (also part of Kendo, Aikido, Judo, Hapkido, etc.) means ‘way of’.
Use of martial arts was restricted to military units.
Normal citizens were excluded from practicing.
As Taekwondo should be a ‘complete’ martial art, the original kicking techniques were completed with Shotokan-karate arm-techniques and Taekwondo was named and born in 1955.
In the 1960’s Taekwondo was still a martial art: barely rules and full contact.
As popularity was booming, rules had to be set, mainly for protection and safety.
Taekwondo became accessible for all people and it was transferred from martial art to a sport.