One way to understand economic bubbles is to read about the two big ones that happened in the recent past:
- The dot.com bubble of the late 20th century:
https://en.wikipedia.org/wiki/Dot-com_bubble
- The housing bubble of the previous decade:
https://en.wikipedia.org/wiki/United_States_housing_bubble
One major difference between the dot.com bubble and today's tech climate is that in the dot.com bubble, many more tech startups went public, exposing many more people to their equities (e.g., via the stock market, mutual funds, retirement funds, etc.). If there's a bubble in privately owned tech companies, the impact will probably not be nearly as severe - the people who'll be hurt are VCs, investors in VC funds and the founders and employees of startup companies. There will probably be a correction in larger tech stocks like Google, Facebook and Apple as well, but they'll probably recover once (1) the markets see that that the problems with startups don't affect these larger companies' earnings very much and (2) money that previously went into VC funds shifts into established tech companies.
"Specifically, I don't understand why a lot of startups being heavily funded will cause a bubble."
The problem (according to the people who think there's a bubble) is that there's too much investor capital chasing too few high-quality startups, so low-quality startups (e.g., ones that have unrealistic business models that have little chance of ever becoming profitable) are getting a lot of money, and they'll eventually collapse and freak out potential investors. That could cause funding for all startups to suddenly get much harder to get. An analogy with the housing crisis is that once the investors ran out of prime mortgages to collateralize, they started putting money in sub-prime mortgages given to homeowners who had little chance of being able to pay them off in the long term.
"How will the bubble burst impact employees who are in a well funded startup?"
Start-ups looking for additional rounds of funding could be hit by investors pulling out of VC funds, making additional funding hard to get. Companies that are still in a stage where they're not profitable could have difficulty staying afloat once they burn through their current round of funding.