I have clay soil. One of the remedy people suggest is to add organic matter. What is organic matter?
Can kitchen scrap like fruit peel, shredded lettuce count as organic matter?
Can shredded plant branched, leaves etc count as organic matter?
Can composted manure bought from big box store count as organic matter?
Thanks.

Adding organic matter alone is not the answer. A clay soil is very dense, it compacts too easily blocking water absorbsion and nutrient flow..
By adding organic matter, it will help a bit but by also working in some rich loam soil and sand will produce a better soil to grow plants in.
Just like it is hard to grow plants in pure sand, it is hard to grow things in a clay rich soil. A mixed soil with good "soil structure" is much preferred.
Organic matter is produced from living things: eggshells, vegetable peels, coffee grounds, etc.
Inorganic things are produced from non living things such as sand, pebbles, glass.

For clay soil, along with the organic matter mentioned, you can also add gypsum. It does not work overnight; takes about 3 years of applying annually to achieve results.
https://www.humeseeds.com/gyps...

I think the reference to "organic matter" was to material that will add texture or porosity to the soil, something the clay lacks.

Organic matter in regard to gardening is anything that can decompose. Kitchen scraps, leaves, pine needles, yard trimmings, contents of mower bag, pulled weeds, mulch, shredded paper, chipped wood, compost. Compost is what organic matter is called when it has decomposed enough to be unrecognizable. Larger pieces of wood & bone will also decompose, but do so at such a slow rate that they are not usually included in composting unless one has space to devote to a long-term pile.

Please know that clay + sand = concrete. Continually adding organic matter really is all that is needed to turn any kind of soil into "black gold" fertile garden soil. There is no need to do anything with it but put it on the soil surface, the way mother nature gardens when no humans are around to intervene. Over time, the soil will become more fertility, and will drain better in times of much rain, while not drying as quickly during times of less.

I've seen this work when I lived in OH in housing developments where the top soil is sold before the neighborhood is built, leaving nothing but the lower layer of solid clay, and in AL where the soil is so sandy that soil is always dusty dry the day after a hard rain.

But don't take my word for it, Dr. Elaine Ingham, soil microbiologist, can explain it in 15 minutes:
https://www.youtube.com/watch?...