Phind's Excellent Balloon analogy will fill in a lot of gaps, for further reading I ercommend the following, and yes the links are under my signature as well. This question is so common its handy to have on hand.
You will find various literature to study and get started in Cosmology under my signature at,
http://cosmology101.wikidot.com/main
particular articles of interest are,
http://cosmology101.wikidot.com/redshift-and-expansion, (note I have a few minor metric corrections to make on this one, but overall still accurate)
http://cosmology101.wikidot.com/universe-geometry
some excellent articles with visual graphs etc. Will definitely clear up some misconceptions.
http://arxiv.org/abs/1304.4446 :"What we have leaned from Observational Cosmology." -A handy write up on observational cosmology in accordance with the LambdaCDM model. ( FAQ style catch up )
http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf: "Misconceptions about the Big bang" also Lineweaver and Davies
if your interested this is a very basic article on relativity its more a historical reference article.
http://www.gutenberg.org/files/30155/30155-pdf.pdf: "Relativity: The Special and General Theory" by Albert Einstein
As far as historical references I've compiled numerous articles. Including
http://arxiv.org/abs/1302.1498 " “The Waters I am Entering No One yet Has Crossed”: Alexander Friedman and the Origins of Modern Cosmology" written by Ari Belenkiy
http://www.astrosurf.com/luxorion/hubble-law-redshift1929.htm
Reprint of one of Hubbles papers
http://apod.nasa.gov/diamond_jubilee/debate20.html
The "Great debate of the 20's" jubilee reprint article avalable
The historical articles will help show how much as changed in the last century. Feel free to ask any questions and enjoy