Why a reference pitch is needed
When instruments play together, they need a shared pitch reference. Otherwise each instrument could be internally “in tune” while the ensemble still disagrees. A4 = 440 Hz is a widely used reference and is specified as the standard tuning frequency in ISO 16.
What 440 actually describes
Hertz is a unit of frequency: 440 Hz means 440 periodic cycles per second. In the normal octave relationship, frequency doubles one octave higher and halves one octave lower. That gives neighboring A pitches of 220, 440, and 880 Hz.
Why a tuner may show another reference value
Many tuners allow calibration of the reference pitch. Ensembles, historical performance practice, or particular instruments may intentionally use another value. When you play with others, the important point is the value everyone has agreed to use, not simply the factory default.
Do not confuse this with transposing instruments
A = 440 Hz defines a real sounding reference pitch. Written transposition is a different issue. A B-flat clarinet can tune to the same A reference as a piano while still using a written pitch system that differs from concert pitch.
A practical check
When you open a tuner, look at the calibration value as well as the detected note. If it was accidentally set to 442 or 438 instead of 440, that can explain why an instrument looks “in tune” on its own tuner but does not match a 440-Hz reference.
If you want to use the reference pitch while tuning in practice, the Tuner is the relevant next step.