Certain verbs and predicative expressions require that an accompanying clause be introduced by the correlative construction consisting of the proper form of тћ plus что.
Such clauses can often be introduced by "the fact that" in English, but often a verb in -ing makes for a smoother translation.
Compare the use of the verb разговђривать (1) with a prepositional phrase and (2) with a clause; just as the noun is in the Prepositional case in (1), so is the word тћ in the Prepositional case in (2):
(1) Онќ разговђривали о языкђх в СССР. They were talking about languages in the USSR.
(2) Онќ разговђривали о тћм, что в СССР говорќли на рђзных языкђх. They were talking about the fact that in the USSR many different languages were spoken.
Listed below are predicative expressions with which the correlative construction is optional: you can introduce the clause simply with что.
довћлен + Instrumental 'be satisfied with'
  Онђ ћчень довћльна мољй рабћтой. She's very pleased with my work.
  Онђ ћчень довћльна (тљм), что ї хорошћ рабћтаю. She's very pleased that I'm doing good work.
привІкнуть к + Dative 'get used to'
  Ћн привІк к похвалђм крќтиков. He's used to the critics' praise.
  Ћн привІк (к томџ), что крќтики егћ всегдђ хвђлят. He's used to the critics' always praising him.
With these words the correlative construction is obligatory:
начђться с + Genitive
  Всё началћсь с тогћ, что ћн поспћрил с нљй. It all started with his arguing with her.
кћнчиться + Instrumental
  Кћнчилось тљм, что Сђша ушёл. It ended up with Sasha's leaving.
знаменќт + Instrumental
  Францџзы знаменќты тљм, что онќ лєбят вкџсно пољсть. The French are famous for liking to eat well.
Here are some useful expression often used with the correlative construction:
дљло в тћм, что 'the fact is,...'
  Дљло в тћм, что Пљтя не умљет пљть. The fact is, Petya doesn't know how to sing.
  Нљт, дљло не в ітом. No, that's not the point.
несмотрї на тћ, что... 'in spite of the fact that...'
  Јтот словђрь ћчень полљзный, несмотрї на тћ, что ћн небольшћй. This dictionary is very useful, in spite of the fact that it is rather small.