The Tekki Kata were originally known as Naihanchi.  
This name was changed to Tekki by Funakoshi to replace the Okinawan name.  He attempted to change the original names of many of the Kata and this is one of the few names that caught on and became commonly used

Tekki Shodan is often credited to Matsumura Sokon of Tomari City, Okinawa, and both Tekki Nidan and Sandan are thought to have been created by Itosu Yasutsune, but as no written records exist (as is the case with any other Kata) we can not be really sure.

Itosu specialised in the Tekki Kata and he taught them to Funakoshi.  He made Funakoshi spend 3 years learning each one saying that whilst they were the easiest of the Kata to learn, they were also the hardest to learn

The name Tekki is composed of two kanji characters.

	Tetsu means iron or steel.
	Ki means ride on a horse, equestrian, or knight.

so some valid interpretations could be

	Steel Horse Rider
	Iron Knight
	Steel Knight

Originally, the stances used in the Tekki Kata were Uchi Hachi Ji Dachi and Naihanchi Dachi but the commonly used stance throughout the three Tekki Kata is now Kiba Dachi or "Horse Riding Stance".   
The Kiba Dachi stance could lead you to believe that the techniques are supposed to be practised for use during battle on horse back.   
A more probable reason for the wide spread use of the stance is its beneficial quality to bad knee conditions 

Funakoshi refers to years of training in the Tekki / Naihanchi kata.  The knees are thought to be strengthened through practice of the Tekki kata due to the emphasis on sideways stepping.  People with bad knee conditions are also frequently recommend to do side to side knee training exercises by therapists.

Students will usually learn the 5 Heian kata one at a time, each time they progress up the belt ranks and then, after reaching the 3rd Kyu, Tekki Shodan is required. 
Tekki Nidan is then not required until the Second Dan examination,  and Tekki Sandan will be looked at in the Third Dan examination under JKA rules.

This is a pity as it takes away the chance for Students to practice the Kata at an early stage of their training

Holding a solid unmoving Kiba Dachi stance whilst performing sometimes 9 upper body attack and defence techniques in position is very difficult.  Add to this you will also have to demonstrate Kime, Breath control and Direction changes - all in the time span it would normally take you to perform 1 or 2 moves in another Kata.  This makes the Tekki Kata perfect preparation for the other more complex Kata