The artist makes use of Celtic myth within this composition, with an injured Tristan being healed by a potion gifted to him by Isolde. She is the daughter of the King of Ireland. They later wished to marry but unfortunately the daughter was forced to carry out her duties and marry King Mark instead. Tristan and Isolde would continue to meet up in secret, such was their love for each other but these rendez-vous would later be discovered by the King. Sadly they would both pass away because of the involvement of others in their lives, in a similar way to Romeo and Juliet. The story would later be repurposed by Malory in the Morte d'Arthur. Stories of romantic couples being impeded by other family members was common in past centuries and also occurred frequently in real life. Thankfully, it is less-so the case now, though still can be found in more traditional families.
That said, this story has also been used by some to warn of the perils of adultery and as a warning to us all of following the right moral path, whatever our animal desires dictate. This painting places the focus most on the cup which Isolde hands to her lover, Tristan. To the left on a table is a round glass which contains the remaining potion. It is a red colour, perhaps suggesting that this is a gift of love. In the background we see a sprawling cliff face, with a castle to the left hand side. This setting outlines the problems of their relationship, often meeting in secret and travelling by ship in order to spend time with each other. They would famously communicate via the colours of flags on each visiting ship.
This painting is instantly recognisable but has sometimes been given slightly different titles - a longer name of Tristan and Isolde Sharing the Potion and also, is some cases, Tristram has been the preferred spelling of the male lead. This has been the case in several notable written publications and so cannot be dismissed as purely a spelling mistake. Whichever your preference, the painting remains one of the artist's most charming and respected artworks. Isolde is also sometimes known as Iseult instead, which is more to do with translation than anything else.