A dump is a place where trash is stored in piles and often buried underground. If you have an old bike that can't be repaired, you might take it to the dump.
Some towns have dumps where residents can freely dispose of garbage, while others require people to pay for the rubbish they bring. You can also call a dump a "landfill," but dump makes sense — it comes from the verb dump, "to toss, drop, or throw away." A figurative meaning of the word is to abruptly and unkindly break off a romantic relationship with someone: "It would be so mean to dump him on his birthday."