When timming, you select, first, the line to use as a "tool", and then select all of the other lines that will be trimmed by that too.
When the two lines cross, the trimming that will be done is pretty obvious: The second line it cut short at the intersection with the first line.

But the two lines don't have to cross for this to occur. Changes to the projection allows or prevents AutoCAD from trimming according to the imaginary projection of the cutting line against the line to be cut.

To experiment, draw a horizontal line and a vertical line that intersect.
Trim one line using the other to demonstrate the TRIM function works as you have it set now.
UNDO so that you can have two crossing lines again.
Now move the horizontal line left or right until it no longer overlaps the vertical line.
command TRIM, select the horizontal line, select an end of the vertical line to be trimmed.
If the vertical line is trimmed by the horizontal line, then PROJECTION was used to trim the vertical line by the projection of the horizontal line.
If the vertical line wasn't trimmed, then projection is turned off. Toggle it on and try again.

Don't forget that you can always Google your way into Autodesk's tutorials with searches like "AutoCAD command TRIM".
Those tutorials are illustrated and include all of the settings in each command.

STF

Hi Sparweb,
Thanks a lot for your insights. Let me check it out and get back.

Hi Sparweb,
I checked against your inputs. But found that what you are talking about is the "extend" option in the edge mode.This extend mode works irrespective of the projection option set (none, ucs, view).
Could you please explain with an another example on the exact application of this option 'Project'? Awaiting your reply on this. Thanks a lot.

It has effect, when you are trimming something within 3D space but not in 2D.
Trim -> Project has three options: None, Ucs and View.
When Project is set to None, trimming lines have to cross each other in the space. Otherwise they will be not trimmed.
When Project is set to Ucs, lines will be trimmed by their projection to XY plane.
When Project is set to View, lines will be trimmed by their projection to current view.

Also could be useful information at https://knowledge.autodesk.com/support/autocad/lea...

Hi Maripali,
Thanks a lot for your insights.Now I understand that it is useful only in 3D.Kudos!