Laxmana was in a fix. He knew that Rama could never get hurt, and secondly he was specifically asked by his elder brother to remain by the side of Sita. If he leaves Sita he disobeys Rama which might bring some misfortune, and if he does not proceed to help Rama Sita is displeased!
The Laxman Rekha
Still, as per the voice of his conscience, he requested Sita to remain calm as no difficulty can come Rama's way. She might have imagined the voice as of her husband's. However, Sita was persistent in her demand that Laxmana must go to Rama's rescue. At last with heavy heart, Laxmana decided to go in search of Rama. But before leaving Sita alone, he drew a line - Laxmana Rekha - that Sita should never cross. (In the event of any one including Sita crossed that Laxmana Rekha the person was sure to get burnt.) Sita promised not to cross the same and after that Laxmana went in search of Rama and the deer.
Ravana Lifts Sita
Here near the hut, Ravana made his appearance as he was sure Rama and Laxmana could/would not come back soon. He also through his Mayawi Power changed himself into a monk - Sanyasin and as the custom went, came to the hut of Sita begging for food. "Bhiksham dehi mai", said Ravana to Sita. (Give me food, O mother.) [In India, today also, it is customary to give alms and food to the begging sanyasin.]
With a tray of some fruits and food Sita came out of the hut at the call of the 'guest' at her door. However, she did not dare to cross the line drawn by Laxmana lest she should get burnt, and hence, she offered the bhiksha from well within the limits of Laxmana Rekha.
Sanyasin Ravana was also equally well aware of the power of that line, crossing of which was sure to see his end! Therefore, pretending to be unhappy at Sita's reservation in serving a 'holy person' from a distance, he shouted, "O noble lady, have you forgotten the lofty and honored tradition of your clan? How can I accept the alms given with reservation and insult! Please come out and give the offerings with propriety and decorum befitting your Aryan tradition."
Thus influenced, no sooner did Sita cross the line than the mighty Ravana took his chance and lifted Sita on his shoulders and fled away. The terrified lady shouted for help, but of no avail. Soon Ravana was flying high in the sky to take aerial route towards his capital city of Lanka. The cry of her help could not reach distant Rama and Laxmana.
Story of Jatayu
But a vulture named Jatayu staying on the nearby tree, and a great devotee of Rama, was quick to respond. He could not keep quiet at the plight of helpless Sita although he knew that he was no match for the mighty Ravana. He was not afraid of him even though it was clear that he would get killed by obstructing the path of Ravana. But he decided to save Sita from the clutches of Ravana at any cost. Taking the name of Rama, he attacked the escaping Ravana within his whole might. His sharp nails and the beak tore flesh from the body of Ravana. Ravana also attacked Jatayu with his sword. The fight went on for quite some time. Jatayu was bleeding from the wounds all over his body. He was exhausted with energy drained out of his wings. At last Ravana cut off his wings and Jatayu fell to the ground.
His mission was not yet complete though. He wanted to meet Rama in his last moments and also tell him about Sita. Therefore, although on his death bed, Jatayu went on repeating the name of Rama - Rama, Rama, Rama.
Laxmana reached the spot where Rama had just killed the demon Marich. Laxmana found Rama unharmed as he expected. He told Rama how Sita forced him to rush for his (Rama's) help on hearing the cry. It did not take long for Rama to put together all the demonic tricks played by Ravana and Marich. He feared that Sita might have landed in great difficulty. Therefore, the brothers rushed to the hut at Panchavati. They were very much apprehensive at the errie silence surrounding the hut.
"O Sita, come out; where are you", they shouted. But how can Sita respond! She was not there. The brothers began their search near and around the hut, in the nearby forest, and went on and on. With tears in his eyes, Rama asked the shrubs and the creepers if they had seen his Sita. He inquired of animals and the trees whether they had any knowledge about Sita.
Then a faint voice of Rama, Rama, Rama was discernible from a short distance. They turn towards the voice and found to their dismay Jatayu lying on the ground reciting the name of Rama. Rama took the wounded bird in his arms and inquired as to who had injured him so ruthlessly. Jatayu told them about Ravana, how he had kidnapped Mother Sita, and had fled to the South. He exhorted Rama to follow the wicked demon and rescue the holy Sita.
At last the pious Jatayu bowed down at the holy feet of Rama and breathed his last in the lap of his chosen ideal. After performing the last rites of Jatayu, Rama and Laxmana started southwards in search of Sita.