Champions League is for the supposedly elite European teams, and the Europa League is just a step down. The Champions League is the biggest European football cup to win.
In the Premiership here in England, the teams that finish in the top four qualify for the Champions League. Fifth qualifies for the Europa League. I'm not exactly how sure it works in other countries but it's a similar principle. Smaller nations with smaller leagues have smaller representation.
Once they qualify for the Champions League they play group stages, same with Europa League. Top two from each group qualify for the knock out rounds, which will be starting soon. Third in the Champions League group gets to play in the knock out stages of the Europa League. Each then play QF'S SF'S then the Final.
Barcelona are favourites for the Champions League but knock out football isn't that straightforward. Liverpool and Juventus are probably the favourites for the Europa League but again, it's not that simple.
Questions?