The Jet Pack is a piece of equipment used in combination with a space suit in order to move around in unpressurised environments - generally outside the space station itself. The jet pack contains its own oxygen supply as well as allowing you to move around in space, so you don't need to take a separate oxygen tank with you.
First, pick up the Jet Pack by clicking on it. Then, using the same hand, double click on the jetpack in your inventory. This will open a window containing the amount of oxygen left in the pack. Click on the 'Restore Flow' button to turn it on, making sure you have a Gas Mask or Medical Mask equipped. Check if you are running on internals - the icon in the top right should be green. Next, remove your backpack by dragging it (in your inventory) from the 'back' slot to your free hand. Then, making sure the correct hand is selected, double click the 'back' slot to strap the jetpack to your back. Finally, right click on the jetpack, and toggle its power to on.