A more thorough explanation:

Definition: To undertake a duty or responsibility. In legal contexts, it means to take over someone else's duty or responsibility.

For example, if Alice assumes Bob's liability for a debt, she takes over Bob's debt. In bankruptcy proceedings, "assume or reject" means to make a decision about a contract or lease that is still valid.

Assume can also mean to suppose something is true without proof.

Legal: Alice assumes Bob's liability for a debt.

Bankruptcy: The company must decide whether to assume or reject the lease on their office space.

Everyday: I assume the store will be open until 9 pm, but I haven't checked their hours.

The examples illustrate how assume can be used in different contexts. In the legal and bankruptcy examples, assume means taking over a responsibility or making a decision about a contract or lease. In the everyday example, assume means supposing something is true without checking.