Matsya Purana- Chapter 260 - Shloka 36 gives us the basic meaning of this three steps of Vamana as "Pervading all the universe" .
तथा त्रिविक्रमं वक्ष्ये ब्रह्माण्डक्रमणोल्बणम्।
बाहुमुपरिष्टात् प्रकल्पयेत् ।। 260.36||
Now about the Vamana form of lord striding the three worlds , as if
pervading all the universe .
Shri Adi Shankaracharya in his Vishnu Sahasranama Bhasya name 530 - i.e. Trivikrama is also explaning the above symbolism behind these three steps of dwarf avatara Vamana.
530 - Trivikrama -The three-stepped
Vyakhya - The three steps were in the three worlds. The shruti (
Tai.Br. 2.4.6) says :" He stepped (the three worlds ) by his three
steps" ; or has walked over the three worlds. The Harivamsha (279-80)
says : The sages have named the three worlds as tri ; and as you
walked them all thrice you are named Tri (vi) krama. .
According to Pancharatra tradition of Vaishnavism the three steps of Vamana symbolise that Vamana (Vishnu) had gone beyond the three vedas. The Wisdom Library page in its meaning of Trivikrama is explaning this with the ref. of commentary of Parashara Bhatta as follows.
These Vibhavas (eg., Trivikrama) represent the third of the five-fold
manifestation of the Supreme Consciousness the Pāñcarātrins believe
in. Note: The name Trivikrama is given to Vāmana who grew up and took
three strides (krama). Parāśarabhaṭṭa Viṣṇusahasranāma vyākhyā on Name
533. gives a different interpreation by quoting a passage the source of which is not known. This means that Viṣṇu had passed through all
the three Vedas or had gone beyond them. The root kram means to walk
over, cross over. The word Vikrama cannot therefore mean studying the
three Vedas but has gone beyond them, prominent in them.