To be tactless is to either be rude (without manners) or inept (without finesse). Either way, it's awkward.
Since people with tact are polite and respectful, tactless people are the opposite: rude and ill-mannered. Interrupting is tactless. Wearing a baseball hat in church is tactless. Not holding the door for someone is tactless. This word has to do with other graces besides social graces too. Being clumsy or lacking in judgment can also be called tactless, and an employee who constantly botches his job and never understands why is also tactless.
adj lacking or showing a lack of what is fitting and considerate in dealing with others
lacking regard for the rights or feelings of others
lacking in refinement or grace or good taste