If I see the Apple Logo is my iphone unlocked?

[Gknee]

I went to itunes held the shift key and downloaded the firmware I had installed on my desktop (3.1.2 7D11). I'm able to use my iphone with T-mobile network to make and receive call and connect to WIFI. I show Cydia, but Rock disappeared and so did the Blackra1n icon. I still show the apple icon on start-up. I am near wifi all the time so I don't have a data plan. Is my phone really unlocked/jailbroke? Can you still connect and download apps on itunes if your iphone is unlocked / jailbroke. Trying to learn all the rules. I had Ping working. Tried to install Swirly MMS trial on Cydia and locked up iphone. Had to restore using the same firmware. Where should I go from here?

[Poseidon79]

I'm confused. You plainly said you are able to use your T-Mobile SIM card. If this is the case you are in fact unlocked. Being jailbroken or unlocked does not affect your ability to buy applications. What generation of iPhone are you using? This determines what you do next after a restore. Most likely you will just use Blackra1n to rejailbreak and/or unlock.

[mikerlx]

^Sure your unlocked if your using tmobile

[Gknee]

I bought it on ebay as an original 2g iphone with firmware 3.1.2 I studied the net and first ran blackra1n then restored using the shift key with the downloaded firmware. The blackra1n logo and the rock disappeared. The phone is working with the t-mobile sim card.
How do you know if you are "jailbroke"? What advantage does this have. I'm able to get apps off Cydia. My bluetooth doesn't seem to work. I'm trying to learn/hack as I go. I'm not sure I understand the terms. I appreciate your time in helping me.

I figured I did something right in the process to be able to use the T-Mobile Sim card, but I'm just not sure exactly what the terms unlock and jailbroke mean. Unlock means able to use another carrier, right? What is jailbroke? and WHY do you do it?