When the clutch plate and friction material no longer have enough friction between them to keep the pair from basically spinning against each other, your clutch is slipping. Absent bad clutch components, a manual can't really slip like an automatic does; there are no bands or hydraulic brakes inside to stop gears from moving and make others engage that can wear out. It's a set of 3 mechanical shafts attached to multiple gears. They are splash lubricated by gear oil, like a differential. Shifting forks engage and disengage each gear individually. They're pretty neat inside.

There is also no torque converter that can slip. Once the clutch is engaged with the crankshaft on a properly operating standard transmission's clutch, the pair are locked together by friction and rotate in sync. Changing gears causes some slippage as you let out the clutch, because the gear ratio is changing and the engine must match the transmission speed, unless you're a really good driver and can match the new RPMs with the gas as you let the clutch out, this always happens. It eventually wears out the friction material.

The sensation will be similar to a slipping automatic. The RPMs will be high, but the car will not feel like it is accelerating correctly.

it's like when you're driving along and if feels like you pushed the clutch pedal in a little, ... but you didn't