The Brahma Purana and the Padma Purana, relate how once, when the demons defeated the Gods, Vishnu hide in the peepal. Therefore spontaneous worship to Vishnu can be offered to a peepal without needing his image or temple. The Skanda Purana considers the peepal to be a symbol of Vishnu. Vishnue is said to have been born under a peepal tree. Some believe that the tree houses the Trimurti – the roots being Brahma; the trunk, Vishnu; and the leaves, Shiva. The Gods are said to hold their councils under this tree, and so the tree is associated with spiritual understanding.
Quoting Wikipedia,
The Skanda Purana states that the Sarasvati originates from the water pot of Brahma flows from Plaksa on the Himalayas. According to Vamana Purana 32.1-4, the Sarasvati was rising from the Plaksa tree (Pipal tree).
Plaksa Pra-sravana denotes the place where the Sarasvati appears. In the Rigveda Sutras, Plaksa Pra-sravana refers to the source of the Sarasvati.
The peepal is also closely linked to Krishna. In the Bhagavad Gita, he says:
"Among trees, I am the ashvattha." Krishna is believed to have died under this
tree, after which the present Kali Yuga is said to have begun. And he will reside in a peepal leaf after Pralayam till the next world is created.

Five-trees (Pancha-vat) are considered sacred in India. They are:
- Fig tree
- A wild fig (Sycamore) tree (Gular)
- Banyan tree
- Pakar (citron-leaved), Indian fig tree
- Mango tree
According to the Skanda Purana, if one does not have a son, the peepal should be regarded as one. As long as the tree lives, the family name will continue. To cut down a peepal is considered a sin equivalent to killing a Brahmin, one of the five deadly sins or Panchapataka. According to the Skanda Purana, a person goes to hell for doing so.
Some people are particular to touch the peepal only on a Saturday. The Brahma Purana explains why, saying that Ashvattha and peepala were two demons who harassed people. Ashvattha would take the form of a peepal and peepala the form of a Brahmin. The fake Brahmin would advise people to touch the tree, and as soon as they did, Ashvattha would kill them. Later they were both killed by Shani. Because of his influence, it is considered safe to touch the tree on Saturdays.
Lakshmi is also believed to inhabit the tree on Saturdays. Therefore it is considered auspicious to worship it. Women ask the tree to bless them with a son tying red thread or red cloth around its trunk or on its branches.
Ref:
- Skanda Purana
- Ficus religiosa(Peepal) : A Phyto-Pharmacological Review