The series follows a boy named Subaru who is pulled from our world into a fantasy land. He welcomes the change and assumes he'll get fantastic powers like the stories he's read, but instead he remains basically himself. The only power he seems to have is that dying sends him back to a previous point in time, reliving hours or days, but he can't tell anyone about it.
I like those concepts - the involuntary time jumps, interesting fantasy world, a hero who isn't an amazing prodigy at combat. Through the initial discovery phase of the series, as Subaru learns about the world and figures out his time jumping power (or curse), it all works together pretty well. The way he manages to ingratiate himself to some fairly powerful people bends the limits of credulity, but that's not uncommon in these kind of stories.
Unfortunately, then the series bogs down. Entire episodes are spent largely listening to Subaru complain about how powerless he is. Characters that were central to early episodes disappear entirely, both friends and enemies, while others pop up almost at random. Even Subaru's main love interest Emelia is absent from large stretches of the series. Hard to do any real character development when everyone but Subaru is constantly fading in and out of the story. And very little progress is made on understanding mysteries that were introduced in the early going.
The last few episodes get back on track, for the most part. There's some moderately interesting action, particularly in the whale fight, and some of the problems laid out earlier are resolved. It still feels like quite a bit is left undone, though. Perhaps there's more complete resolutions in the manga, but in the anime the story feels unfinished.
I watched all of Re:Zero because of the interesting hooks - the time jumps, a comparatively weak hero, exploration of a new world. Sadly, the execution doesn't hold up to the promise. If the hooks sound like your thing, try it out; otherwise, you're probably better passing it up.