Stabilisation counters hand shake so you can use slower shutter speeds without blur.
In-body (IBIS) and lens (OIS)
In-body stabilisation moves the sensor and works with every lens, including adapted and vintage ones. Lens stabilisation moves elements inside the lens and is especially effective with long telephotos. Many systems combine both for the best result, such as Canon's coordinated IS, Panasonic's Dual I.S. 2 and OM System's Sync IS.
How much it helps
Makers quote 5-8.5 stops. In practice, expect enough to hand-hold a wide lens at 1/4s or slower with care. Results vary by focal length and technique.
What it can't do
Stabilisation steadies the camera, not the subject. A child running at 1/30s will still blur. For moving subjects, you need a fast shutter speed.
Which cameras skip it
Some cheaper APS-C bodies, such as the Canon EOS R10, Canon EOS R50 and Sony A6400, lack IBIS. With those, choose stabilised lenses for low light and video.