In more detail
mAh measures charge: the current a battery can supply multiplied by how many hours it can supply it. The energy stored also depends on voltage, which is why watt-hours (Wh = V × Ah) are the fair way to compare batteries. A lithium-ion cell has a nominal voltage of about 3.6 to 3.85 V. Ratings are for new cells at room temperature; real capacity falls in the cold, at high discharge currents and with age, and cells are commonly rated to keep about 80% of their capacity after several hundred full cycles. Runtime is roughly capacity × usable fraction / load current: 2,000 mAh at 100 mA is 20 hours in theory, 16 hours with 80% usable.
Why it matters
Power-bank capacities in mAh are quoted at the internal cell voltage, not at the 5 V the USB port delivers, and conversion losses come on top, so a "20,000 mAh" bank never puts 20,000 mAh into a phone. Airline rules for lithium batteries are written in watt-hours (spare batteries up to 100 Wh are generally allowed in carry-on luggage), so the Wh figure is the one to look for on the label.
Example
Phone battery: 5,000 mAh × 3.85 V = 19.25 Wh
Power bank: 20,000 mAh × 3.7 V = 74 Wh
Delivered at 5 V, 85 % efficient: 74 × 0.85 = 62.9 Wh → 62.9 / 5 = 12.58 Ah
The bank delivers about 12,580 mAh at 5 V, at most 3.3 phone charges (62.9 / 19.25), fewer once the phone's own charging losses are counted.