A host of a trill symbiont gains access to the memories of the symbiont and therefore those of all the previous hosts.
The existence of the symbionts was for centuries a closely guarded secret (DS9 anthology: The Lives of Dax) and well into the 24th century the relationships between Trill humanoids and symbionts was a source of much political and social upheaval on the planet Trill and beyond. (DS9/TNG comics: Divided We Fall)
When a symbiont was not inside a host body, they made use of electrochemical signals to communicate with others through the liquid they lived in. A joined symbiont was also capable of communicating with its non-joined counterparts by being submerged in the fluid breeding pools on the Trill homeworld. This provided a direct form of communication between the two but not on the same level of sharing knowledge as that which a Joining was capable of providing.
While typically symbionts only communicated with and took Trill as hosts, it was possible for them to communicate with Humans at least through extended contact. This was done through matching the symbiont's bioelectric patterns with those of the other individual. However, this required direct tissue contact between the nerves of the person with those of the symbiont. (DS9 novel: Time's Enemy)
As symbionts grew older, they eventually became unable to take hosts and would sink to the bottom of the pools where they would become caretakers for the Annuated, eventually these symbionts would grow to become Annuated themselves over a period of 20,000 years or more. (DS9 novel: Trill: Unjoined)
In the Mirror Universe, the Trill Symbionts were infected with a hostile parasitic intelligence. Emperor Spock ordered all the symbionts, save for Dax, exterminated in order to stop them becoming a threat to the Empire. This has left Curzon Dax as the only joined Trill. (TOS - Mirror Universe novel: The Sorrows of Empire)
See Also: Trill symbionts for a list of symbionts.