I assume you are developing an Add-In tool in ArcMap. The following are some high level steps you probably want to do.
1) From your IMap you can get the parcel layer in TOC by index or enumeration. Find the layer and cast it to IFeaturelayer.
2) IFeaturelayer has a mehtod called Search which you will need later.
3) You tool has a mouse down event which has parameter of XY (this is the screen display XY).
4) Inside the mouse down event handler you will need to transform XY to map XY. Look at IScreenDisplay, you can get there using your map document's ActiveView property.
5) With map XY, you will be able to create a point geometry.
6) Use this point in a ISpatialfiler.
7) Pass ISpatialfilter into the Search method from step 2 to get a Feature cursor.
😎 Cycle thourgh the feature cursor because there could be 0 to many polygons selected.
9) Find value of the feature by passing in index of the field you're looking for.
10) Use the value as you wish to display to GIS Technician.