This is the original definition, and it is genuinely a time. Each coupon date is weighted by how much of the bond's present value that payment represents. A zero-coupon-bond has a Macaulay duration exactly equal to its maturity because there is only one cash flow.
Higher coupons pull duration down, since more of the money arrives early. Longer maturities push it up. It is the input from which modified-duration is derived.
Example: a 3-year bond, 5% annual coupon, yielding 5%. Present values are 47.62, 45.35 and 907.03 for years 1, 2 and 3. Macaulay duration is (1 x 47.62 + 2 x 45.35 + 3 x 907.03) / 1000 = 2.86 years.
Related: duration, modified-duration, zero-coupon-bond, coupon