Until recent decades, the only things that changed visibly within a human lifetime outside our solar system were supernovae, and the apparent positions of nearby stars (and that only barely measurably).
Modern equipment has uncovered many objects of several different kinds that change visibly in human time-scales. Here are a few examples.
Still the only things that change outside our galaxy in human lifetimes are supernovae (well, and cepheid variable stars…).
Eta Carinae is the largest star known in our galaxy, being some 30 to 50 times as massive as our sun. It formed only a few millions of years ago, and hasn’t long to live—it is expected to explode soon.
The bell-shaped object of a recent minor outburst of the star. It still changes visibly within months.
Unfortunately not a video, but a “difference of two images taken 17 months apart”
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This is light from a flash made by the star, reflected off dust and gas in the vicinity of the star, moving as successive observations are made. So, this isn’t material moving, it is light moving through material.
The star pulses every 40 days or so, waves of light from those pulses pass through surrounding dust and are echoed back to us.
See: Light echoes whisper the distance to a star
Our local big black hole, weighing in at around 3 million solar masses, can’t be seen at visible wavelengths of light, but has a very big effect on surrounding stars.
These are big stars, behaving like comets orbiting the black hole. But some are in very fast orbits, 11 years or so, although their orbital radii are several times that of our solar system.
Main site at Max-Planck-Institut für extraterrestrische Physik, with further animations
By the Chandra X-ray observatory: it looks like an artist’s rendition of a hypothetical accretion disk and jet, but it is an actual observation.
The jet is clearly moving. In the accretion disk, the motion is that of shock waves moving through the disk.
Accretion disks and gas jets are a common of occurrance in several rather different situations. Besides the big jets associated with distant black holes (where the disk is too small to be seen) and some neutron stars, they are often found about young stars nearby.
Scorpius X-1 was the first discovered extraterrestrial X-ray source. It is relatively nearby (9000 light years distant), and is thought to consist of a medium-sized star and a neutron star orbiting one another every 19 hours. The neutron star would strip material off its companion, which would accrete to its surface, periodically producing an accretion disk and jet.
The jet consists of two beams, one pointed toward us, one away. Here we see a clump in the lobe pointed at us, moving very rapidly—at nearly the speed of light.
From our vantage point, the size of the source and the lobes is very small. These pictures were made using numerous radio telescopes; only such equipment could resolve these small details.