You already know modal verbs such as müssen, können, and sollen in their objective, basic sense: müssen for obligation ("must"), können for ability ("can"), sollen for recommendation or instruction ("should"). At this level you learn that these same verbs, with no change in form, can carry a completely different, subjective meaning: instead of describing an objective state of affairs, they express the speaker's degree of certainty or stance toward the truth of some information. Context alone determines which meaning is intended.
When you say Er muss zu Hause sein, you don't mean he is obligated to stay home — you mean you're almost certain, based on evidence you have, that he is home, equivalent to "he must be home." This subjective use forms a whole scale of certainty, with a different verb for each degree: müssen expresses near-total certainty based on strong logical inference; dürfte, the Konjunktiv II form of dürfen, expresses a very high probability, though less definite than müssen; könnte and mag express a mild possibility or an open guess.
Sollen carries a different kind of meaning altogether, unrelated to degrees of certainty: it reports a claim or rumor the speaker has heard from someone else, without endorsing it — equivalent to "it is said that" or "supposedly." Conversely, wollen in its subjective use reports a claim the subject makes about themselves, and it usually carries a shade of doubt or disbelief from the speaker — roughly "claims to."
To express this subjective meaning in the past, you don't put the modal verb itself in a past tense; instead you keep it in the present and add what's called Infinitiv II — the Partizip II of the main verb followed by haben or sein: Er muss es vergessen haben ("he must have forgotten it") — notice muss stays in the present while the past meaning is carried entirely by vergessen haben.
This double use of the same verb for two entirely different meanings has no single equivalent in many languages, which tend to use separate, unrelated phrases for each degree of certainty. As a result, learners often misread subjective muss as obligation ("he has to be home" instead of "he must be home"), or mishandle the subjective past by conjugating the modal verb itself in the past tense — musste vergessen instead of the correct muss vergessen haben with Infinitiv II.