Generally, no—just as you can’t travel when confined to jail. But you may be able to travel to work, or get a court-approved exception, in unusual circumstances, to the no-travel restriction.
“House arrest” is really a misnomer—being confined to one’s residence is not done when someone is arrested. Instead, it’s an alternative to a sentence for a crime, for which the arrestee has pled guilty or been found guilty. Instead of being sent to jail or prison to serve a sentence, the defendant is ordered to remain at his residence for a prolonged period of time. House arrest is not a novel concept (Galileo was confined to his home when he suggested, contrary to church teachings, that the earth revolved around the sun).
House arrest, also referred to as intensive supervision, is typically monitored through the use of a GPS device that is attached to the prisoner, usually around the ankle. The signals are monitored; if the wearer ventures too far afield, the local police are alerted.
House arrest programs can be quite flexible, imposed at the beginning of a sentence or later, and revoked at any time if the offender fails to meet conditions. Typical conditions include meeting regularly with a probation officer, maintaining steady employment, remaining crime-free, and returning home after work. Attending school and religious services, going to court, seeing a doctor, and performing community service are common allowances, and other locales may be approved by the prisoner’s probation officer.
Occasionally a house arrestee will ask a court for permission to travel for an extraordinary reason, such as to attend a family funeral. It's up to the court or probation office whether to grant these requests.
House arrest has many advantages for society. The state saves the enormous amount of money it costs to house a prisoner. And because most house arrest programs require the prisoner to be employed (and presumably have health insurance), the state saves on medical costs, too. In addition, families of prisoners can continue to be supported, rather than going on welfare. Prisoners who have restitution orders (a court order telling the defendant to pay for the victim’s direct financial losses that resulted from the crime) are in a position to repay them, as well as any court-ordered fines.
On the other hand, some argue that the public is less protected when a convicted criminal is allowed to remain relatively free, even though non-violent and low-risk offenders are usually the only candidates for the programs.
You shouldn't do anything to jeopardize your status while under house arrest. Doing so could expose you to additional criminal sanctions and penalties. If you are uncertain as to the rules of your house arrest, or if you need to be able to leave your house for any reason not sanctioned by the terms of your confinement, you should consult with an experienced attorney who can help you to understand your rights and get the necessary permissions to travel.