Lord Ayyappa

Mahishi, sister of Mahishasura out of anger performed severe austerities to the creator deity Brahma, who granted her desired boon of only being capable of being slain by the son of Vishnu and Shiva. Satisfied by the impossibility of such an event, Mahishi, possessing the prowess of both the goddess of prosperity and power, quickly overran Svarga, taking the throne of Indra for herself and forcing the devas into exile. Brahma arranged for Dattatreya to assume the form of Sundara Mahisha, a handsome bovine, who was able to enchant the lovestruck Mahishi enough to lead her away from heaven to the forests of Earth. After the events of the Samudra Manthana, Shiva was enraptured by the beauty of Mohini, the female avatar of Vishnu. The child who was born from their union was Ayyappan, the one destined to slay Mahishi.

It is believed that he was born from the Swethabindu (sweat drop) when Mohini and Shiva danced. He is referred to as hariharasutha (son of hari and hara). Ayyappan was found at the banks of river pamba with golden bell named Mani tied to his Kantha (neck) and he is referred to as Manikanta. Rajasekhara, king of Pandala has found him and adopted him as he has no sons. He was raised with love and devotion, unaware of his divine lineage. His upbringing in a human kingdom reflects his earthly connection and his eventual divine purpose. Way later the king was blessed with a biological child.

When Manikantha was 12 years old, the king wanted to formally anoit him as the heir. However, the queen objected to it, favoring her younger biological child. The queen feigned an illness, asking for the milk of a tiger to cure her illness. No warrior couldn’t get the same and hence Manikantha volunteers and goes into the forest, where he confronts the demoness Mahishi, whom he kills and returns back riding a tigress. The king realizing Manikantha's special ability recognizes him to be a divine being and resolves to make a shrine for him. Manikantha transforms into Ayyappan and shoots an arrow to denote the place for the shrine and the arrow falls at Sabarimala.

Irumudi

It is believed that when Ayyappa is leaving to forest, his father has given him a two compartment blueish bag having one coconut and pooja items in one and compartment, food items useful in the journey in the other. This is known as Irumudi (Iru means two, mudi means pouch and kettu means knot or bundle. It is a two compartment bundle carried on the head by the pilgrims/devotees of Lord Ayyappan at Sabarimala. Irumudi is the travel kit of the devotee to the temple. This has to be carried only by those who observe the austerities or vratha of 41 days.)

Ayyappa held irumudi in his head and started to forest to get the milk.

"Those who had the vratha with the Irumudi kettu only are allowed to proceed to the Sannidhanam (place of worship) at Sabarimala climbing the 18 steps (holy 18 steps)."

Makarajyothi

Makara Jyothi is a star worshiped by pilgrims at Sabarimala Temple in Kerala on Makara Sankranti (Pongal) every year. It is believed that the deity Ayyappan asserts himself as Makara Jyothi to bless his devotees. Makara vilaku is a holy ritual fire, lit at a specific time, on a hill east of the sannidhanam.

Scientific explanation: The sun is constantly moving between the Tropic of Cancer and Tropic of Capricon which is called in the Indian context as Uttarayanam and Dakshinayanam. Makara Sankranti falls in the period when the Sun, which is in the Tropic of Capricon in the Southern Hemisphere, has started moving northwards towards us in India. Which means we start having longer days. We are starting to come out of the cold season to warmth and it is this Change, new beginning of the seasonal cycle that we celebrate.

Yogapatta

Yogapaṭṭa literally means ‘cloth of yoga’. This is the band of cloth (or belt) used for holding the crossed legs firmly in position while practicing yogic meditation. It goes around the two legs at the knee level, the legs being slightly raised. It may be wound round in other ways also. when we see Lord Ayyappa, the state of sitting may be called Arddhasana, Yogapadasana or Yogarudha Siddhasana. This status of sitting reveals the mood of asceticism, the Tapobhava. There is a binding of knees with a cloth in the style of sitting of Lord Ayyappa while he is holding the Yogamudra. The feet of a yogi who is in tapovrutti (in the ascetic calmness) will never let move away his legs. The Pandala king brought a golden belt and tied it around the legs of the Lord so that the Lord felt comfortable to remain in the posture and also remained there enshrined in the Sabarimal temple forever to bless the devotees. This is why we find the golden belt tied around Ayyappan’s legs.

For more insights on deities leg postures, refer this external article

Lastly why Ayyappa called as Ayyappa? - In some parts of southern India, 'Appa' means father, and 'Ayyan' (Ayya/Arya in Telugu) signifies a title of respect. Thereby, the name stands for a revered senior deity of the area.

Consider reading the Travancore Devasthanam Article on Ayyappa as well - https://sabarimala.kerala.gov.in/about-lordayyappa