No, you will not own the device at the end of your leasing term. However, you do have the option to buy your phone at the end of the term by paying the balance off.
Cell phone leasing plans are payment plans where a carrier charges you each month to "rent" their phone.
A plus with leasing plans include options to upgrade your device earlier than the typical 2-year contract plan.
If you want to own the phone at the end of the term then you would need to take out a finance plan rather than a lease. It works in the same way but will cost a few dollars more each month as you are paying off the full value of the phone.
I have included some links to show you a couple of different phone options when taking the leasing route. Leasing plans for a Samsung Galaxy s6, a Samsung Galaxy s6 Edge and a Samsung Galaxy Note 5 are listed below. Each of these leasing plans are through Sprint as they are the only carrier to offer a lease. Most of the other carriers offer finance / monthly installment plans where you own the phone at the end.
Click Lease on the Ways To Pay line between the phone plan specs and the results.