The fundamental difference lies in the orientation of the optical components:  

Upright Microscope:

Light source and condenser are located below the stage.

Objectives are positioned above the stage, pointing downwards towards the specimen.

Typically used for examining:

l Thinly prepared slides

l Small samples

l Fixed specimens

Inverted Microscope:

Light source and condenser are positioned above the specimen.

Objectives are located below the stage, pointing upwards towards the specimen.

Designed for:

l Examining samples in larger containers  

l Easier sample manipulation

l Observing living cells in culture