What kind of tube valve is this?

That is a Presta valve. Bikes often come with two types of valves, Presta and Schrader. Schrader valves are the same type of valve you find on car and truck tires. Higher end road and mountain bikes normally have Presta valves, while most entry level bikes have Schrader valves because Schrader valves are practically indestructible, and very easy to use; however, Schrader valves require a large hole through the rim, and are much bulkier than Presta valves.

The pump you are trying to use is probably meant for Schrader valves only. You can either buy a new pump meant for Presta valves, or you can buy a small attachment, which will allow you to use the pump you have now.