''Beauty and the Beast'' is an old and much-loved fairt tale, or folk tale, of Europe, with parallels in other cultural/folk traditions in Asia and Asia Minor too.
In the past, adults and children all used to listen and read and just enjoy fairy tales and maybe also learn vital 'lessons' from them subconsciously; but today, increasingly, there's a trend towards analysing fairt tales/fables for 'interior meaning' and 'latent symbolism', especially along psycho-analytical (Jungian) lines.
This story is no exception and some of the major symbols in it include:
1. The Rose: a symbol of beauty, love, passion, fidelity, spirituality, wisdom etc
2. Forest: Represents in Jungian psychology, the 'feminine' -- the dark, deep, unknown, erotic side in particular; also, stands for depth, darkness and lack of clarity, confusion etc
3. Cottage: Represents humbleness, simplicity, innocence, peace and tranquility, contentment.
4. Castle/servants: Symbolic of closeness, chastity, dominance, a 'masculine' and warlike symbol, exerting control over and 'locking in' the feminine/women; with the 'help' of subservient forces, servants/slaves, etc
5. Youngest daughter/child: In traditional folk lore and fable, the younget sibling, male or female, is the 'good' or 'virtuous' one usually, and is sometimes stupid and lucky or beautiful/goodlooking and 'worthy' and 'pure' etc.
There are many, many other symbols too, and the link shared below might be of some help in adding some more. Good luck