Ter·ri·to·ri·al wa·ters. Internat. Law The waters under the territorial jurisdiction of a state; specif., the  belt (often called the marine belt or territorial sea) of sea subject to such jurisdiction, and subject only to the right of innocent passage by the vessels of other states.
    Perhaps it may be said without impropriety that a state has theoretically the right to extend its territorial waters from time to time at its will with the increased range of guns. Whether it would in practice be judicious to do so . . . is a widely different matter . . . . In any case the custom of regulating a line three miles from land as defining the boundary of marginal territorial waters is so far fixed that a state must be supposed to accept it in absence of express notice.    --W. E. Hall.

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 territorial waters
      n : the waters surrounding a nation and its territories over
          which that nation exercises sovereign jurisdiction [ant:
          high sea, high sea]