"eternity" - time which never ends, has no limits
"infinity" - refers to time or space (+length, height) also numbers
To me, "eternity" is more poetic than "infinity" is. It's like "wiecznosc" v. "nieskonczonosc". They can be used interchangeably, but somehow it sounds nicer when we say "I am yours for eternity" than "I am yours for infinity"... The last one is what Einstein could have said... ;o)