A quick summary of the plot. Roy Batty (RIP Rutger Hauer), a Replicant--an android with human-like sensibilities and (rapidly deteriorating) biology-- escapes to earth with his fellow androids (they'd been banned from earth after committing "mutiny" in space).
The Replicants want to live. The humans say they're dangerous (some uncanny valley discomfort might also be part of their rejection--this is further explored in the sequel, BR 2049). Detective Deckard (Harrison Ford aka, the Blade Runner) is sent to hunt and kill the Replicants. Batty, a combat android, is considered the most violent/leader of the group and is killed last. Dying, he utters the lines to a terrified and confused Detective Deckard:
"I've seen things you people wouldn't believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhäuser Gate. All those moments will be lost in time, like tears in rain. Time to die."— Roy Batty, Blade Runner
The rest is movie cult history. The Tears in the Rain monologue remains as confusing today as it was then. Though Hauer had repeatedly explained that he performed a throwaway operatic ramble, scholars and mere mortals alike continue to analyze the meaning of those words.
My own interpretation is that the line isn't throwaway, though it is meant to be confusing (the Replicants are misunderstood). Batty was essentially telling Deckard that his experiences--the things he has seen--don't matter ("tears in the rain"). Why do these things not matter? Because he's a Replicant deemed unworthy of life.
In a way, he was saying, you'll never know me nor do you care to know me (my personal interpretation). He may also be saying, aren't humans a culmination of our lived experiences? If so, then why do my experiences not make me worthy of life? The experiences "moments in time" that he references (Orion's shoulder, C-beams and Tannhauser Gate) are his pride, but they mean nothing (not to the humans who only care to kill him).
Let's explore these personally referenced experiences a bit.
The first is the easiest to understand--"attack ships on fire off the shoulder of Orion"--Orion is the hunter constellation-- Orion's shoulder was one of the locations in space where the mutiny/battle took place--Batty was a soldier in the war (The Replicants were banned from earth after they took part in a rebellion in space--a bloody off-world mutiny, as it's described). Batty is most likely referencing this battle in his speech--attacks ships on fire off the shoulder of Orion; c-beams in the dark near Tannhauser Gate. C-beams are "cesium or cutter beams"-- a type of particle beam weapon used in space combat" -in other words, he watched laser or light beams "glitter in the dark"-- light beams/lasers were being fired in the battle.
The last reference is the one that puzzles people the most. What is Tannhauser Gate? This one is harder to interpret, and I will approach it two ways. First things's first. Tannhauser was a 13th century German poet, whose exploits took on mythical/legend turns, inspiring plays and operas.
The legend of Tannhauser (not the real man) goes like this: One day he discovers a gate to the underworld (Venusberg). He spends a year indulging all the vanities of flesh, drink and sin. Out of guilt, he returns to the real world and visits the Pope at the Vatican, seeking remission. The Pope explains he has none to give. Tannhauser leaves (supposedly returning to Venusberg) and is never heard from again. Tannhauser's portrayed in the operas/legends as a man who found no absolution for his sins. The main interpretation suggests Batty fancies himself Tannhauser, a fallen man deemed too out of touch with the mortal world to be accepted in it.
Before I explore Batty's affinity to the mythical Tannhauser, let's look at the literal interpretation of Tannhauser Gate. Batty speaks of "watching C-beams glitter near Tannhauser Gate," suggesting it's a place/region in space, similar to Orion's shoulder. Currently, there are no constellation in the sky named after Tannhauser--unlike Orion. This is not to say that in the universe of Blade Runner there isn't such a location. Nonetheless, if Tannhauser Gate is a region in space, then why is this region named after a fallen man of legend?
The easiest analysis is that Tannhauser Gate may be an exosolar point of entrance/exit, perhaps between our solar system and elsewhere. Think, for example, of the Kuiper Belt, a region existing on the periphery of our solar system. It may also be a station or port, not unlike say, Deep Space 9 in the Star Trek universe, a space station set up next to a wormhole to keep tabs on whatever comes through.
If the Replicants were fighting to return to the planet from the deep of space, but had to push through a blockade (ships?) or patrolled region that stands between the deep chaos of space and earth's orbit, then Tannhauser Gate makes perfect sense as a name. The "gate" discovered by the mythical Tannhauser is a portal between the world of mortals and the underworld.
It may very well be true also that Tannhauser Gate is not the official name of the place, but what Batty personally calls it, further illustrating his feelings of empathy with the mystical man. Tannhauser expressed remorse about indulging in Venusberg's sins--the reason he left--though Venusberg was described as a place of great indulgence. It does appear that Batty sees "outer space" akin to the underworld, for better or worse. On this topic, his opinion seems almost contradictory, to the point where one might suggest he regretted the space mutiny/his life of violence in space (in an earlier scene, he admits that he's done "questionable things" that perhaps makes him unworthy of extending his life).
In way, war is beauty and pleasure for Batty, a Nexus-6 Replicant (combat model and trained soldier). He poetically describes watching ships on fire and c-beams (a war weapon) glitter--basically treating destruction as if it is a firework display--something awe-inspiring. These are proud "moments" for him--they gave his life meaning; hence, it's what he laments as he lay dying; so why then does he want to leave the chaos of outer space for earth?
To return to the personal. What Batty has in common with the mythical Tannhauser is a desire to return to the world of mortals. Tannhauser is there to reclaim his humanity. Batty is there to extend his life/to live--a gift denied to Replicants. To some extent, Batty is seeking his humanity, and acting on a very real desire to live (he even saves Deckard's life near the end, suggesting his deep respect/desire for the thing called "life").
Tannhauser visits the Vatican in search of redemption and forgiveness, but is turned away (believed to have returned to Venusberg, his underworld of sinful indulgence). Batty makes it to earth, but is killed (denied extended life). Both fail to find what they seek. Batty is Tannhauser, a fallen being who seeks absolution in the world of mortal but finds condemnation ("time to die").