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How to explain an income discrepancy to the IRS? 
The IRS doesn't tax "increased wealth" They tax Revenue -- income.  If this money or property came to you as a gift, you would owe no tax on it but the giver probably would owe gift tax.  If it came to you as a loan, you would owe no tax on it but the lender would owe tax on any interest you pay (and must charge at least minimal interest, though they could give that to you as a gift and possibly not have it be taxable). But if came as payment for goods or services or investment or anything of that sort, and you aren't demonstrably tax-exempt, it is income and you are responsible for declaring it as such and paying tax on it.