Based on your question, It sounds like you want your users to be able to choose multiple options from a lookup or dropdown.
From a UI perspective, the difference between a simple and multi-select lookup seems minor. In reality, the difference is quite significant because you are no longer storing a single data point. Therefore you need to create a separate table to store all of the connections between your current table and the lookup table. This connecting table is called an associate table.
For more instructions on creating a Multi-Select lookup please see: Multi-Select Lookups