I have seen this floating around the internet and especially on Reddit the last couple of days, to what extent is this true? Or not true?
The short answer to your question is no. Easter is pretty obviously not an absorbed Pagan tradition. It's a celebration of a specific historical event the date of which is given explicitly in the New Testament, and it's directly tied to the Jewish Passover. It's also being celebrated very early. Fun fact, the dating of Easter was one of the first big controversies of the early Church.
On "Easter", Eostre was a Germanic (not Roman) fertility goddess whose existence is only attested to by the Venerable Bede, -- 8th century English monk, Doctor of the Catholic Church, and possessor of one of history's great names -- in his work on time, which you can check out here. Bede says in a passage describing the conventions of the English:
Eosturmonath has a name which is now translated "Paschal month", and which was once called after a goddess of theirs named Eostre, in whose honor feasts were celebrated in that month. Now they designate the Paschal season by her name, calling the joys of the new rite by the time-honored name of the old observance.
So, Easter isn't a pagan holiday, but the name was taken the name of a month which was derived from the name of a goddess. Think Thor--->Thursday, Woden-->Wednesday. This is also written at least 600 years after our first recorded celebrations of Easter and, as noted above, exclusively talking about English people.
Easter is a Christian holiday taking place in the spring commemorating the resurrection of Jesus Christ. It, like many other Christians holidays, has taken and adapted facets of various springtime holidays in other religions. Its name is taken from Eostre, a Germanic goddess of springtime, fertility, and rebirth (possibly from an association with the rising sun).
Similarly, Christmas is a Christian holiday taking place in late December (in most denominations) celebrating the birth of Jesus Christ. It adapts facets of various pagan traditions, such as gift-giving from the Roman Saturnalia.
To say that Easter "is really" a pagan tradition is not only completely inaccurate, but also highly disrespectful and dismissive, as well as an extreme oversimplification of what is in fact a fascinating history of syncretization and religious adaptation.
(Note that I'm not accusing OP of doing anything of this sort, he or she is very responsibly asking for clarification on the claim. I am accusing many nameless denizens of reddit of doing such.)
A follow-up question if I may - wedgeomatic and Zhankfor's replies make it clear that Easter is a Christian tradition. But did it replace an already existing European tradition? That is, did Romans/Germanics/Celts already celebrate something roughly around the same time prior to Christianization?