Blank verse is quite simply poetry written with a standard meter but no specific rhyme scheme. When someone listens to blank verse being read, it generally has a sing-song sound or recognizable rhythm. Free verse, on the other hand, has no standard rhyme or meter (see Walt Whitman).
Shakespeare is often credited as the master of blank verse, and if you study any of his plays, the majority of each play (excluding prose portions to show common or low-class speech or couplets, etc.) is written in blank verse.
In regards to writing your own two lines of blank verse, do not rhyme the end words, and make sure that you "clap it out"--in other words, both your lines should have the same number of syllables, and if your professor wants exact blank verse, the accentuated syllable of each word needs to be the same in each word (i.e., iambic pentameter or other specific meters).