http://www.avvo.com/attorneys/20007-dc-eric-koester-1214516/...
There are several pages of articles & you might have to read and re-read a few times. It's dense, but clear.
Founders usually purchase all their shares up front, so this term says that the company can buy a percentage back if they leave before 4 years.
A: "I want to sell to a third party."
Company: "We have a repurchase right."
A: "Well, I'm selling for $10 a share."
Company: "We don't think that's the right price."
A: "What do you think is the right price?"
Company: "We would need to hire an auditor to determine that, and you would have to pay for him."
Auditors for independent valuation should only come in to play when there is no price, for instance, when a block of shares is offered to existing shareholders or the company and they can't agree on a valuation.
Drag along / tag along clauses definitely can complicate this.
In the case of Sam Altman's founder-friendly term sheet, what you're describing is covered by the 'ROFR/Co-Sale Agreement' section.
The repurchase right here refers to what happens if a founder leaves before their four-year vesting schedule is up - the company has the right to repurchase their unvested stock, almost certainly (although his term sheet doesn't specify) at the original near-zero issue price.
Since founders typically own 100% of their stock for tax purposes (hold it for a year, only have to pay long-term instead of short-term capital gains), the only way companies can subject founders to a vesting schedule is to have the option of buying the unvested portion back.
The standard mechanism for this is accelerated vesting - I think Nivi wrote the definitive bit on it, here:
1) if you want to sell your stock to someone else before IPO, the company has to approve the sale. If they don't like who you're selling to (which could just be because they don't want voting shares belonging to outside people), they can choose to buy it back instead. If they don't like your price (too low or too high), then you and the company have to negotiate a 'fair' price.
2) The company has the option, but is not required, to buy back any unvested shares that you have already exercised if you leave.