What is the significance of inserting discordant notes in written music?

Discordant notes are a kind of musical spice. 

Most people like the taste of mayonnaise in their food, and most people enjoy vanilla ice-cream for dessert.  But imagine if every night your dinner was made with mayonnaise, and every night your dessert was vanilla ice-cream.  Boooooring, right?

Your meals need spice.  Sometimes salt and pepper, sometimes curry, sometimes burning-hot jalapenos.  And then sometimes, when you go back to good-old mayonnaise and vanilla ice-cream, you'll appreciate that more, too.

Music is the same.  A steady diet of C-chords is pleasant but boring.  A flatted fifth (G-flat) in the middle of a C-scale is a little spicy and mysterious.  Duke Ellington was known to arrange pieces that had a bass instrument play an E at the same time that an alto saxophone played an F--two notes that are right next to each other and are not part of any "normal" chord.  The result: interesting, spicy, attention-grabbing, unforgettable.

Of course, you can go overboard.  A piece that has nothing but discordant notes can give you a big headache. Unless you're interesting in creating a musical replica of a headache, it's best to compose using a reasonable balance of both harmonious and discordant notes.