Quasi means almost or near to. Quasi–Static process means very nearly static process. Let us consider a system of gas contained in cylinder. The gas held by a moving piston. A weight W is placed over the piston. Due to the weight , the gas in cylinder is compressed. After the gas reaches equilibrium, the properties of gas are denoted by p1, v1, t1. The weight placed over the piston is balanced by upward force exerted by the gas. If the weight is removed, then there will be unbalanced force between the system and the surroundings. The gas under pressure will expand and push the piston upward till it touches the stops. The properties at this state after reaching equilibrium are p2,v2,t2. But the intermediate states passed through by the system are non-equilibrium states which cannot be described by thermodynamic coordinates. In this case we only have initial and final states and do not have a path connecting them.
Suppose, the weight is made of large numbers of small weights. And one by one each of these small weights are removed and allowed the system to reach an equilibrium state. Then we have intermediate equilibrium states and the path described by these sates will not deviate much from the thermodynamic equilibrium state. Such a process, which is the locus of all the intermediate points passed by the system is known as Quasi-static process. It means, this process is almost near to the thermodynamically equilibrium process. Infinite slowness is the characteristic feature of quasi-static process.