How does the inactive state work?
When your account is set to Inactive, Postcrossing will not select your address to receive postcards. As soon as you set it back to Active again, you will receive all postcards that your account should had received during that time.
So if you know you are going to be away from your address for more than a week (for example: on holidays, a business trip, etc.), you should set your account to inactive (on your account settings) in advance, so that postcards stop being sent to you. This way, other members will not be kept waiting for a long time to have their postcards registered.
You can still send postcards while your account is in the inactive status — Postcrossing will just hold back sending you cards until you're ready to receive them.