Mantra’ means energy and ‘Thaaraka’ means ‘a thing that takes you across’. Rama mantra takes you across the sea of worldly life and helps you cross it to reach the other world.
Narayana and Shiva are our main deities. Moola mantra for Narayana is Om Namo Narayana. Moola mantra for Shiva is Om Nama Shivaya
In Narayana Moola Mantra, “Om Namo Narayana," the life of the mantra lies in the letter "ra. If the letter "ra" is removed, the moola mantra becomes inauspicious. Om Namo Narayana becomes Om Namo Nayana
In the Shiva moola mantra, “Om Nama Shivaya”, the life of this mantra lies in the letter "ma". If the letter "ma" is removed, the moola mantra becomes inauspicious.Om Nama Shivaya becomes Om Na Shivaya
The life packed these 2 letters of the moola mantras combine to form the Thaaraka Mantra – “RAMA” (Ra+Ma)"
‘Saint Tyagaraja explains this in his Kriti - Evarani Nirnayinchiri
Siva mantramunaku 3ma jIvamu
mAdhava mantramunaku rA jIvamu(y)I
vivaramu telisina ghanulaku mrokkeda
vitaraNa guNa 4tyAgarAja vinuta
The meaning of the above is as follows
“For the Siva mantra (OM namaSSivAya), ‘ma’ is the soul; for the vishNu mantra (OM namO nArAyanAya), ‘rA’ is the soul; I salute the great personages who understand this detail”
Let's Think of the glory of Rama, involve in his Japa and seek liberation from our sins