Simple Definition:

Modal auxiliaries are a type of helping verbs [verbs that work together with the main verb] that express different meanings such as ability, possibility, permission, and necessity. They modify the main verb in a sentence to indicate the speaker’s attitude, obligation, or expectation.

Examples:

• She can [has the ability to] swim.
• They might [possibly] come to the party.
• You should [have necessity to] study for the test.
• We must [have the obligation to] finish this project.

Very Simple Definition:

Modal auxiliaries are special words that help us talk about what we can do, what might happen, and what we should or must do.

Examples:

• She can swim.
• They might come to the party.
• You should study for the test.
• We must finish this project.