The share-basis is about accommodation pricing. It does not mean that you share a room with a stranger.
"Twin-share" is where two people occupy a hotel room (open-plan style) or other accommodation such as an apartment, usually a couple or two friends. This is the normal way accommodation is priced. The price is shared between two people. Most accommodation properties (eg. hotels) offer rooms with king, queen or double beds. Most offer the option of "twin" beds as well which actually means two single beds to accommodate singles sharing, couples wanting space and so-on.
"Triple share" is where three people occupy the accommodation and share the price. "Quad-share" is where four people occupy the accommodation and share the price. Family apartments and hotel rooms usually include a king, queen or double bed and one or more single beds to handle triple and quad-share arrangements. Sometimes other bedding configurations are available as well.
Some accommodation providers, especially in very popular holiday locations, have higher room rates for busy holiday periods (usually spring and summer holidays). We must make an allowance for those price variations if applicable.
A "single supplement" applies to single travellers who want a room to themselves. Because the price is not shared, a "single supplement" applies. This additional amount is based on the single covering the entire accommodation component of the trip that would normally be split between two or more people.