A spell that has a casting time of "1 full round" takes up all your actions for that round, but you get to use the full effects of that spell, whatever they may be.
A spell that takes "1 round" to cast, is technically a full round action, but is actually taking even longer to cast. You're still continuing to cast the spell while everyone else in the initiative order acts again, and you finish the casting just before your next turn. The spell doesn't come into effect until the beginning of your next turn, and you can act normally. You can also be attacked by other people while you're doing this, which may force one or more concentration checks in order to complete the spell.
The most common spells with 1 round casting times are the summon spells. So, for example, you have a sorcerer casting "Summon Monster I"
Round 1: Sorcerer begins casting. This uses up all his actions.
Round 2: Spell complete. A celestial eagle appears and begins to move at the sorcerer's direction. The sorcerer also has his full range of options for this round, so he can move, cast again, etc.
It also might go like this.
Round 1: Sorcerer begins casting. This uses up all his actions.
Enemy fighter gets to go. Notices the sorcerer is casting, and shoots an arrow at him, which hits. The sorcerer takes damage, and is forced to make a concentration check to finish casting his spell. He succeeds.
A second enemy fighter gets to go, and also shoots an arrow at the sorcerer, hitting him and forcing a second concentration check. This time the sorcerer fails the check and the spell fizzles.
Round 2: Nothing is summoned, but the sorcerer can act as normal.
So, unlike normal casting, where you only generally need to worry about concentration checks if you're casting defensively, grappled, or drawing attacks of opportunity, a spell with a 1-round casting time offers more opportunities for foes to interrupt the casting. A spellcaster attempting this will likely want to make sure that he is unseen, or otherwise protected before beginning.