You just bought a touch lamp, which you can turn on and off by touching the base of the lamp. You might wonder if your lamp requires a special bulb, but it doesn't. You can use any standard bulb for your touch lamp.
Your touch lamp works by detecting the presence of your hand on its base. The light bulb is not a part of the lamp and therefore does not affect how your lamp works.
Even if your touch lamp is a floor lamp, or a table lamp, or if it screws into the wall, you still do not need a special bulb. The lamp's mechanisms are internal and the bulb does not affect them.
You can identify the type of light bulb that your touch lamp uses by reading its owner's manual. It will tell you to purchase a standard bulb, which you can find at hardware, grocery and other stores. Be sure to select the correct wattage when purchasing your bulb.