The water pump circulates coolant through the engine and radiator. When its seal or bearing fails, you get a coolant drip from the weep hole, a grinding or whining noise from the front of the engine, or a temperature gauge that climbs because coolant isn't moving. Left alone, the bearing seizes, the belt shreds and the engine overheats.
On many engines the water pump is driven by the serpentine belt and sits on the front of the block, which makes it a straightforward on-site job. On engines where it's driven by the timing belt, it's a bigger job that's usually done together with the belt. The mechanic will tell you which your engine is when quoting.
Mobile-Car-Repair.xyz has a local mobile mechanic in 250 cities doing cooling system work. Reach out through your city page at the first drip.