You can gift an app by purchasing the app using your iTunes account, then send the recipient a promo code for the app. The recipient can then download the app without paying for it themselves. The process can be done in iTunes or through the App Store mobile app.
From your device, launch the App Store and find an app you want to gift. Scroll to the bottom and tap on the Gift This App button. You will see a summary of the app then hit Next to enter the recipient information. The last screen will show you an order summary. If all is correct, tap on Buy Gift and the recipient will be sent an email with the gifted app.
From iTunes, find the app you want to gift and and click on the arrow to the right of the Buy App button. A drop-down menu appears with the Gift This App option on top. You will then be taken to a page that lets you choose whether you want the gift emailed or you can print it and hand-deliver it. Then enter the recipient information and confirm the purchase by clicking Buy Gift.