My mother (US citizen) was working in Japan for many years and accumulated $300,000.00 in savings. She transferred this money to her account in the USA to purchase a house a little over a year ago. The INS has recently wrote her a letter asking about this money.

My question is:
1- Does my mother have to pay taxes on this wire transfer/amount?
2- Because she didn't know she had to declare this amount to the INS, would she be penalized for this?

Your mother is going to have to document where the money came from. The government wants to know the source of the money. The goal is to prevent money laundering. That is why financial institutions report large cash deposits, or other deposits when the source is not clearly known.

As to the tax issue, as a US citizen, your mother has to pay taxes on income. If it was earned in prior years and not reported, penalties and interest are likely. If the money was not income, and she can provide evidence of that, there should not be any taxes or penalties.