A T-shirt company bought a new packaging and tacking systems for $100,000. The formula V = 100,000(1 – 0.125)models the value of the system, V, in dollars, after depreciation for y years. In this formula, what is the meaning of the term (1 -0.125)?

You have the folowing formula:
V = 100,000(1 - 0.125y)
for the value of the new system of the T-shirt company.
The factor (1 - 0.125y) means that each year the value of the system decrease in a factor of 0.125, which is equivalent to a decrese of 12.5%.
HENCE:
the value of the system will decrease by 12.5% each year