An offer is a communication of interest in buying or selling an asset. In other contexts, it might refer to the act of making something available for sale.
For example, a retailer might offer a men's watch for $2,000, meaning that the retailer will sell the watch for that amount. However, a customer might come into the store and offer $1,500 for the watch, meaning that the customer is expressing an interest in buying the watch for that amount.
Offers make the business world go around, because a fundamental rule of markets in a capitalistic economy is that a product or service is worth only what someone is willing to pay for it. Anybody who has tried to sell an asset in a down market has probably learned this rule the hard way.