I was going through A320 AFM and came across Thrust modes. I was not able to understand why thrust is in thrust mode during climb and descent because we climb or descent with a constant speed. So according to me it should be in constant speed mode.
A normal climb is performed with a constant thrust1 and a constant speed. The autothrust system will take care of the constant thrust (THR CLB) and the autopilot (or flight director for manual flight) will take care of the constant speed. This means you maintain the target speed by pitching up or down. If the speed is below target, pitch down to increase speed, and vice versa.
The same is true during a descent. The autothrust will maintain idle thrust (THR IDLE) and the autopilot or flight director will maintain the target speed by pitching down.
During cruise, where the altitude remains constant, the target speed needs to be achieved by setting the correct amount of thrust. Now the autothrust system is responsible for maintaining speed and will show SPEED or MACH on the FMA (Flight Mode Annunciator).
The A/THR modes are selected automatically in conjunction with the AP/FD modes (except ALPHA FLOOR).
(Airbus A320 FCOM - Autoflight - Flight Guidance - A/THR Modes)
1The actual thrust produced by the engine is not constant, it depends on altitude. The FADEC will compute a thrust rating limit depending on the selected thrust lever position:
The FADEC computes the thrust rating limit for each thrust lever position [...]. If the thrust lever is set in a detent, the FADEC selects the rating limit corresponding to this detent.
(Airbus A320 FCOM - Powerplant - Thrust Control System - Thrust Rating Limit)