An evidential marker is a grammatical indication of what
evidence a speaker has for what they say. In English we resort to roundabout ways of showing this, such as 'they say' or 'should be' or 'is supposed to be' for things we've heard, but in some languages the marking is an obligatory part of grammar, just as English has to mark present tense or past tense.
For example, in Quechua Paymi runasimita riman and Paysi runasimita riman both mean 'S/he speaks Quechua'. The difference is that the -mi suffix shows that I know this from personal experience, whereas -si means I know this because I learnt it from someone else. There is a third evidential marker, -cha, which indicates uncertainty: Paycha runasimita riman means 'S/he probably speaks Quechua'.
It is important not to be led astray by the lack of this feature in English. The two former sentences both mean 'S/he speaks Quechua'. It would be exaggerating the difference to translate one as 'I know s/he speaks Quechua' and the other as 'I heard s/he speaks Quechua'. When you're saying these in Quechua you're not saying you know anything or you've heard anything, you're simply stating a fact about the person: they speak Quechua. There's no particular reason to suppose the hearsay -si form is in any way uncertain. After all, there's the -cha form to indicate actual uncertainty.
Translating them into English with extra bits to show up the difference runs afoul of pragmatics as expressed in Grice's maxims. The simplest thing to say is just 'she speaks Quechua', so if you use extra words and say 'I've heard she speaks Quechua', that pragmatically implies you couldn't just say 'she speaks Quechua'. And why, thinks your hearer, couldn't you say this? Probably because you weren't really sure: well, I've heard she does, but... So it's important to stress that the evidential marker in Quechua is just a grammatically necessary choice. It does not contain anything corresponding to 'so I've heard' or 'they say' or 'I'm not sure'.
Tibetan has verbs 'to be' that distinguish personal knowledge and hearsay. Turkish has a suffix -miş that indicates hearsay, but can also be used for related evidential purposes: even if the speaker and the hearer can see the fact, it might indicate surprise, as in English if George turns up unexpectedly you might say to him, 'Well, it seems George is here.'
The Californian language Wintu has a particularly rich battery of evidential grammar, as do a lot of American languages. In Wintu the unmarked form is for direct visual experience. For sensory experience that's non-visual, and for inference from intuition, they use the suffix -nthEr. For inference from observed results use -ree, for inference from previous experience use -?el, and for hearsay evidence use -kee.
In Kashaya, another Californian language, a conversation might open with a speaker using the -wela form, meaning they're doing the action or they've just been doing it. It then moves into the -wa form, which is for ordinary factuals.
Kiefer, F., 'Morphology and Pragmatics', in Spencer and Zwicky (eds), 1998, The Handbook of Morphology, Blackwell
Coronel-Molina, S., 1989, Quechua Phrasebook, Lonely Planet