Any fabric consists of warp and weft yarns. Weft ones are located perpendicular to warp ones. Yarns can be 1-ply, 2-ply, 3-ply and even 4-ply (very rarely). 2-ply means that each yarn (thread) consists of two yarns tightly twisted together. 3-ply = 3 yarns twisted together, 4-ply = 4 yarns, etc. 2-fold and double-twisted = 2-ply.
Turnbull & Asser shirt. 2-fold 120’s cotton fabric by Thomas Mason.
2-ply, 3-ply and 4-ply fabrics are more durable and resistant to wear than 1-ply ones (with all other things being equal). They’re also less prone to ‘pilling’. Please note: some brands use term 2-ply for 1×2 or 2×1 fabrics. Genuine 2-ply fabrics are always 2×2, i.e. warp yarns are 2-ply, and weft yarns are 2-ply too. Always prefer 2×2 fabrics to 1×2 or 2×1 ones. Remember that today even very respected brands of fabrics (like Albini) can offer 1×1 fabrics. Some brands, however, produce only 2×2 and 3×3 fabrics (for example, Alumo).
Here are some brands who offer ready-to-wear shirts under 100 USD made of 2-ply fabrics (but they can be 2×1 or 1×2): Boggi, Cotton Experts (often 2×2), Charles Tyrwhitt, Harvie & Hudson, Hawes & Curtis, Kamakura (2×2!), Marks & Spencer (only Sartorial and Luxury lines), Suitsupply, Thomas Pink, T.M.Lewin. Please note: these brands can also offer shirts made of 1-ply fabrics.
If you want to learn more about shirt fabrics, I recommend to read ‘ A Discourse on Shirt Fabircs‘ by Alexander Kabbaz.