In order for your company to submit for I-485 Application for Adjustment of
Status for you they have to show your H1B petition has been approved and
file a copy of the approved H1B petition with the I-485 application and
$1,010 fees, along with copies of all your identity docs (passport copies,
birth certificate, marriage certificate, divorce certificates if any, etc.
for you and all your family members).
In the meanwhile, if you are in status with your H1B Visa, you may travel
inside US and out without problems. Make sure to take your original
approval notice approving H-1B status with you when travelling (or its copy
if your employer cannot give you the original) and show it along with your
passport and employment authorization at US customs when returning to US.
If you are too close (within 30 days) to the expiration of the date of your
H1B approval, I would not recommend travelling. If your status has expired
and your employer has applied for extension but you have not yet received
the approval for the extension, please do not leave US.