Great question. I'll be drawing heavily from Mary Beard's "SPQR" and cannot recommend it enough if this is a topic you are interested in. So let's begin:

It’s important to understand that the Etruscans are a somewhat mysterious people to us. Thus the shortest answer to your question is it’s complicated and there are no neat and clean answers. From what we know, it is obvious that they exerted heavy influence on early Roman culture, including the introduction of the Greek alphabet (which would later morph into the familiar Roman alphabet). Roman myth references several Kings of Rome that were of Etruscan decent. Furthermore, it is likely that the Roman pantheon borrowed heavily from the Etruscan religion and perhaps most important, most of Rome’s first encounters with Greek culture came via the Etruscans and not the Greeks themselves. Alas, we have yet to decipher ancient Etruscan so what scant artifacts we have from them are impossible to read. Thus everything we know about the Etruscans comes from 1 of two sources: the Romans themselves or archaeologist unearthing Etruscan sites.

Looking at the first source of information on the Etruscans, the Romans, we see a few problems. To begin with the Romans would have been incredibly biased. So we have to take everything they say with a grain of salt. Plus to make matters worse Rome was sacked in the late 300s BC by the Gauls and thus most writings about the Etruscans (and the early history of the city itself) were lost. Most Roman sources on the Etruscans were written centuries after they had disappeared and as you can imagine they were based largely on myth and hearsay. As a side note the Emperor Claudius was said to have written an extensive Etruscan dictionary, which would be an incredible find if you rediscovered it.

So let us look at the complicated relationship between Rome and Etruria. The Etruscans were not really a unified political entity but a group of city states that had a shared cultural bond. Their heartland was the area north of Rome in what is now modern Tuscany (indeed the word Tuscany is derived from Etruscan). While Rome was in its infancy the Etruscans were by far the dominant force on the peninsula. If you were alive during this time and had to bet which group in Italy would rise to dominate the known world, you would’ve put everything you had on the Etruscans. They had extensive trading links throughout the Mediterranean and enjoyed a prolific artistic culture as evidence by elaborate painted tombs you can still visit today. Rome, with its mud and stick buildings huddled around what was basically a marsh on the Tiber River were a cultural backwater. It is easy to see how these earliest of Romans borrowed so much from their wealthy neighbor’s culture

However Rome’s position between the Etruscans and the Greek colonies on the southern tip of Italy, coupled with its location on the only forge of the Tiber River contributed to its rapid rise in fortune. And as its wealth and population grew it started to view its Etruscan neighbors as rivals to what the Romans believed was their destiny to rule the world.

As to what happened to the Etruscans, in short they were conquered by the Romans. The word conquered is admittedly a bad word to use here as Rome more or less assimilated the Etruscans into their expanded web of alliances. Seeing as the two had very similar cultures, it did not take long until all vestiges of authentic Etruscan culture were abandoned in favor of the ascendant Roman identity. On top of all that, the Etruscans were never as political organized as the Romans and the Roman army ran roughshod over their county.

It is a great question and I tried to answer with as much brevity as possible so inevitable I had to make some generalizations. Again there are some really great books on this subject you look into.

You can also see this question from a couple of months ago.