A harmonically closed section ends on the tonic chord ($\left.\text{I}\right.$). A harmonically open section typically ends on a non–tonic chord like $\left.\text{V}\right.$, but could also end on $\left.\text{IV}\right.$.
In an AABA form, the A sections are usually harmonically closed, ending on $\left.\text{I}\right.$, and the B section (or bridge) is usually harmonically open, ending on $\left.\text{V}\right.$.
For example, the verse and bridge on “We Are the World” are harmonically open (end on $\left.\text{V}\right.$) while the chorus is harmonically closed (ends on the tonic chord, $\left.\text{I}\right.$).