You're going to have to provide more detail as to the context of the conversation to get a better response, but my best guess is they were referring to the combination of the standard deduction and personal exemptions:
Standard Deduction is $6,200 for Single filers and $12,400 for Married Filing Jointly. Personal Exemptions are $3,950 per person. Extrapolating out a bit, if the context involves a single parent of one child, that would mean a standard deduction and two personal excemptions, or $14,100.
In fact, this person said "Your taxable income would be ~$34k" and you yourself said "...bringing my taxable income down to approximately $34k," so what's the discrepancy?