What exactly is Bioshock Infinite about?

[Cicero]

So I'm not sure if I'd like the game. The era it seems set in seems very fun. What's the game about (small summary) and is it free roam? What weapons or powers do you have?

[Rayquaza]

It's amazing what Google can get you.

http://lmgtfy.com/?q=Bioshock+Infinite

BioShock is set during 1960, in the fictional underwater city of Rapture; the player learns of its history through in-game audio recordings scattered throughout the game.[27][29] The city was planned and constructed in the 1940s by Objectivist business magnate Andrew Ryan who wanted to create a utopia for society's elite to flourish outside of government control. Scientific progress greatly expanded, including the discovery of the plasmid ADAM created by sea slugs on the ocean floor; ADAM allowed its users to alter their DNA to grant them super-human powers like telekinesis and pyrokinesis.

At the start of the game, player-character Jack is a passenger on a plane that goes down in the Atlantic Ocean in 1960.[32][33] As the only survivor, Jack makes his way to a nearby lighthouse that houses a bathysphere terminal that takes him to Rapture.[34]
Jack is contacted by Atlas via radio, and is guided to safety from the Splicers. Atlas requests Jack's help in stopping Ryan, directing him to a bathysphere where he claims Ryan has trapped his family. When Jack encounters a wandering Little Sister and its Big Daddy, Atlas urges Jack to kill the Big Daddy and kill the Little Sister to harvest her ADAM for himself; Dr. Tenenbaum overhears this and intercepts Jack before he harms the Little Sister, urging him to spare the child, providing him with a plasmid that would force the sea slug out of her body.[35] Jack eventually works his way to the bathysphere, but Ryan destroys it before Jack can reach it.

Weapons: http://bioshock.wikia.com/wiki/BioShock_Infinite_Weapons (Another Google Search Link)
Contents [hide]
1 Barnstormer
2 Bird's Eye
3 Broadsider
4 China Broom / Heater
5 Huntsman /Burstgun
6 Paddywhacker
7 Pepper-Mill
8 Sky-Hook
9 Triple R / Repeater
10 Pig / Hail Fire
11 Behind The Scenes

[Aves]

If it follows suit with the old Bioshock games, it won't be free-roam until near the end of the game. There will probably be plasmids (which is like magic I guess) and guns such as a machine gun, pistol, wrench. If you want an idea of what to possibly expect, play Bioshock. Really great game with a great story and gameplay. One of my favorite games that I've played.