The phrase "mouth of the River Thames" refers to the wide, tidal estuary where the Thames meets the North Sea—roughly between Southend-on-Sea (Essex) and the Isle of Grain (Kent), extending seaward past the Thames Estuary into the outer estuary/Thames Gateway.
In geography, a river mouth is "the wide lower end of a river where it flows into a sea, lake, or another river" (Definition 1). For the Thames, this isn't a single point but a funnel-shaped estuary ~5.5 miles (9 km) wide at its broadest, where freshwater mixes with saltwater over tidal cycles. The Thames Barrier (near Woolwich) marks the practical upstream limit of tidal influence; the "mouth" lies well downstream.
The entry also lists a dictionary-style second definition: "Entrance" (Definition 2), followed by an unrelated idiomatic example: "He's got a big mouth" (colloquial for someone who talks too much or reveals secrets). This appears to be a concatenated dictionary entry rather than a coherent explanation.
So, "mouth of the River Thames" = the tidal estuary entrance to the North Sea—a busy, engineered, ecologically rich gateway.