heart, liver and lungs: These are the internal organs of a sheep, traditionally used as key ingredients in haggis.
recites: To recite means to say something from memory, especially in a formal way, such as a poem or a speech.
toasts: In this context, to toast means to raise a glass to drink in honor of someone or something, often with a specific congratulatory or celebratory phrase.
raising their glasses: This is the physical action accompanying a toast, where people lift their drinking glasses to show respect or good wishes.
tatties and neeps: These are traditional Scottish accompaniments to haggis. 'Tatties' is a Scots word for potatoes, and 'neeps' is a Scots word for turnips (or swede).
accompanied by: This means that something is served or presented together with something else.
'Auld Lang Syne': This is a famous Scots song, traditionally sung at the end of Burns Night celebrations and other occasions, meaning 'old long since' or 'times gone by'.