Don't worry about asking basic questions, we all have to start somewhere and wrapping your mind around the concept of vlans can be challenging coming from the world of non managed switches.
When people say "the default vlan," they're almost always referring to vlan1. The reason that most people get confused is that they think of the vlan 1 as being this special thing that is like any other vlan, but in reality it isn't. In reality vlan 1 is the vlan you're used to dealing with on non-managed switches. In fact, if you take your cisco switch with the default, out-of-the-box config and connect it to any other non managed switch you could buy at an office supply store, all ports on both switches will be in vlan 1. For now, think of vlan 1 as no vlan at all.
Now... to access the GUI you had to set an IP address on the switch. If you do a show run and look at the config, you'll see the ip addess you set under...
interface Vlan1
This interface is not a physical port on the switch, rather a virtual interface that is attached to "the default vlan" and all ports not configured as access or trunk ports are part of this vlan. That is why you could access the GUI from any port other than the one you set as an access port for your PC.
The easiest way to think about vlans is dividing your single switch up into differant individual switches that operate independantly. In fact, you could accomplish almost the same thing by using multiple unmanaged switches instead of vlans. The main purpose of vlans is to enable us to conserve resources by reducing the number of switchs we need and also be able to reduce the amount of cabling we need in our facility. When used in conjunction with routers or firewalls, vlans reduce the number of physical interfaces we need on these devices. Imagine a large network with 50 network segments. Without vlans, you would need at least one switch for every segment and either a router with at least 51 physical interfaces or 50 individual 2 interface routers. From a cabling perspective, imagine you had two server closets and you needed to get network traffic between those two closets for those 50 network segments. Without vlans, you would have to run 50 cables between the closets and have at least 100 switches!
So hopefuly, that explains vlan 1, the "default vlan," but what about the other vlans...
Lets take your example. By creating another vlan (we'll call it vlan 2 for now since you didn't specify the vlan number you created) you now effectivly have two switches. One switch operates on "the defaul vlan" and the other on vlan 2. Any ports that you don't issue the switchport access vlan X command on are part of the vlan 1 switch and any ports you make access ports on vlan 2 are part of the vlan 2 switch.
Now what about the switch's IP address that you assigned? That IP address is attached to a virtual interface in vlan 1. The virtual interface isn't a physical port on the switch, rather it is an interface that the switch itself can use to have access to a specific vlan. This is why your PC could get to the switch's GUI on any port but the port you made an access port on vlan 2. Vlan 2 has no access to vlan 1 because it is logically a differant switch and the switch itself has no way of communicating with a PC on vlan 2 because it doesn't have an interface to connect it to vlan 2.
If you wanted to access the GUI from your access port on vlan 2, you would need to create a virtual interface on vlan 2 and give the switch an IP address on that subnet. For example...
Switch(config)#interface vlan 2
Switch(config-if)#ip address x.x.x.x y.y.y.y
Switch(config-if)#no shutdown
Switch(config-if)#exit
Now the switch would have an IP address on vlan 2 with which it could communicate with your PC on it's access port in the same vlan. One note here... I never use the GUI on any Cisco device so I'm not totally sure but I believe the GUI is accessible from all vlans on the switch as long as the switch has an interface with a valid IP on that vlan. If that is the case, you should now be able to access the GUI using the IP address assigned to interface vlan 2 from you PC on an access port on vlan 2.
Hopefully this info helps clear things up a bit.
